knowledge_graph_model.json

[
  {
    "source": "等价无穷小",
    "target": "极限计算",
    "weight": 0.9
  },
  {
    "source": "洛必达法则",
    "target": "极限计算",
    "weight": 0.9
  },
  {
    "source": "原函数",
    "target": "变限积分求导",
    "weight": 0.9
  },
  {
    "source": "变限积分求导",
    "target": "含参变量积分求导",
    "weight": 0.85
  },
  {
    "source": "换元积分法",
    "target": "含参变量积分求导",
    "weight": 0.8
  },
  {
    "source": "二阶常系数齐次线性微分方程",
    "target": "二阶常系数非齐次线性微分方程",
    "weight": 0.95
  },
  {
    "source": "特征值与特征向量",
    "target": "特征多项式",
    "weight": 0.9
  },
  {
    "source": "特征多项式",
    "target": "矩阵特征值计算",
    "weight": 0.85
  },
  {
    "source": "事件独立性",
    "target": "概率加法公式",
    "weight": 0.85
  },
  {
    "source": "函数奇偶性",
    "target": "原函数的奇偶性",
    "weight": 0.9
  },
  {
    "source": "原函数",
    "target": "原函数的奇偶性",
    "weight": 0.9
  },
  {
    "source": "左右极限",
    "target": "极限",
    "weight": 0.9
  },
  {
    "source": "极限",
    "target": "连续性",
    "weight": 0.95
  },
  {
    "source": "连续性",
    "target": "可导性",
    "weight": 0.95
  },
  {
    "source": "定积分",
    "target": "傅里叶系数",
    "weight": 0.85
  },
  {
    "source": "傅里叶系数",
    "target": "傅里叶级数",
    "weight": 0.9
  },
  {
    "source": "奇偶延拓",
    "target": "狄利克雷收敛定理",
    "weight": 0.85
  },
  {
    "source": "狄利克雷收敛定理",
    "target": "傅里叶级数求和",
    "weight": 0.95
  },
  {
    "source": "矩阵乘法",
    "target": "矩阵的秩",
    "weight": 0.85
  },
  {
    "source": "矩阵的秩",
    "target": "行列式",
    "weight": 0.9
  },
  {
    "source": "随机变量的独立性",
    "target": "正态分布的线性组合",
    "weight": 0.9
  },
  {
    "source": "正态分布",
    "target": "正态分布的线性组合",
    "weight": 0.9
  },
  {
    "source": "极限概念",
    "target": "等价无穷小替换",
    "weight": 0.9
  },
  {
    "source": "极限概念",
    "target": "洛必达法则",
    "weight": 0.9
  },
  {
    "source": "导数",
    "target": "洛必达法则",
    "weight": 1.0
  },
  {
    "source": "导数概念",
    "target": "洛必达法则",
    "weight": 0.85
  },
  {
    "source": "变限积分求导",
    "target": "含参变限积分求导",
    "weight": 0.9
  },
  {
    "source": "换元积分法",
    "target": "含参变限积分求导",
    "weight": 0.85
  },
  {
    "source": "特征方程",
    "target": "二阶常系数齐次线性微分方程",
    "weight": 0.9
  },
  {
    "source": "特征方程",
    "target": "待定系数法求特解",
    "weight": 0.85
  },
  {
    "source": "二阶常系数齐次线性微分方程",
    "target": "非齐次微分方程解的结构",
    "weight": 0.85
  },
  {
    "source": "待定系数法求特解",
    "target": "非齐次微分方程解的结构",
    "weight": 0.85
  },
  {
    "source": "矩阵的秩",
    "target": "矩阵乘积的秩",
    "weight": 0.9
  },
  {
    "source": "矩阵的秩",
    "target": "齐次线性方程组有非零解的条件",
    "weight": 0.9
  },
  {
    "source": "齐次线性方程组有非零解的条件",
    "target": "行列式为零的判定",
    "weight": 0.85
  },
  {
    "source": "矩阵乘积的秩",
    "target": "行列式为零的判定",
    "weight": 0.8
  },
  {
    "source": "矩阵乘法",
    "target": "行列式计算",
    "weight": 0.8
  },
  {
    "source": "随机变量的独立性",
    "target": "方差的性质",
    "weight": 0.95
  },
  {
    "source": "期望的性质",
    "target": "正态分布均值参数",
    "weight": 0.85
  },
  {
    "source": "方差的性质",
    "target": "正态分布方差参数",
    "weight": 0.85
  },
  {
    "source": "正态分布",
    "target": "标准化",
    "weight": 0.9
  },
  {
    "source": "标准化",
    "target": "标准正态分布",
    "weight": 0.95
  },
  {
    "source": "标准正态分布",
    "target": "对称性",
    "weight": 0.85
  },
  {
    "source": "正态分布的标准化",
    "target": "标准正态分布的对称性",
    "weight": 0.9
  },
  {
    "source": "多元复合函数求导法则",
    "target": "多元隐函数求导",
    "weight": 0.9
  },
  {
    "source": "多元复合函数求导法则",
    "target": "隐函数方程组求导",
    "weight": 0.9
  },
  {
    "source": "隐函数求导",
    "target": "隐函数方程组求导",
    "weight": 0.95
  },
  {
    "source": "行列式计算",
    "target": "克莱姆法则",
    "weight": 0.9
  },
  {
    "source": "克莱姆法则",
    "target": "隐函数方程组求解",
    "weight": 0.85
  },
  {
    "source": "隐函数方程组求导",
    "target": "隐函数方程组求解",
    "weight": 0.95
  },
  {
    "source": "偏导数",
    "target": "格林公式",
    "weight": 0.9
  },
  {
    "source": "闭合曲线构造",
    "target": "格林公式",
    "weight": 0.9
  },
  {
    "source": "格林公式",
    "target": "二重积分",
    "weight": 0.95
  },
  {
    "source": "曲线积分参数化",
    "target": "对坐标的曲线积分",
    "weight": 0.85
  },
  {
    "source": "格林公式",
    "target": "对坐标的曲线积分",
    "weight": 0.95
  },
  {
    "source": "曲线积分",
    "target": "曲线积分与路径无关",
    "weight": 0.9
  },
  {
    "source": "曲线积分",
    "target": "参数方程法计算曲线积分",
    "weight": 0.9
  },
  {
    "source": "二阶导数",
    "target": "一阶导数单调性",
    "weight": 0.95
  },
  {
    "source": "一阶导数单调性",
    "target": "一阶导数符号判定",
    "weight": 0.85
  },
  {
    "source": "导数运算",
    "target": "函数单调性",
    "weight": 0.9
  },
  {
    "source": "函数单调性",
    "target": "函数最值",
    "weight": 0.9
  },
  {
    "source": "构造辅助函数",
    "target": "导数运算",
    "weight": 0.8
  },
  {
    "source": "函数单调性",
    "target": "不等式证明",
    "weight": 0.85
  },
  {
    "source": "定积分的物理应用",
    "target": "变力做功",
    "weight": 0.9
  },
  {
    "source": "定积分的微元法",
    "target": "变力做功",
    "weight": 0.9
  },
  {
    "source": "定积分的计算",
    "target": "变力做功",
    "weight": 0.85
  },
  {
    "source": "定积分的微元法",
    "target": "定积分的计算",
    "weight": 0.9
  },
  {
    "source": "矩阵数乘",
    "target": "特征值与特征向量",
    "weight": 0.85
  },
  {
    "source": "矩阵相等",
    "target": "方程组求解",
    "weight": 0.9
  },
  {
    "source": "方阵的行列式",
    "target": "特征值的性质",
    "weight": 0.85
  },
  {
    "source": "特征值的性质",
    "target": "伴随矩阵的特征值",
    "weight": 0.95
  },
  {
    "source": "行列式的性质",
    "target": "行列式按行展开",
    "weight": 0.8
  },
  {
    "source": "行列式按行展开",
    "target": "代数余子式",
    "weight": 0.9
  },
  {
    "source": "正定矩阵的定义",
    "target": "齐次线性方程组的解",
    "weight": 0.85
  },
  {
    "source": "齐次线性方程组的解",
    "target": "矩阵的秩",
    "weight": 0.9
  },
  {
    "source": "样本均值",
    "target": "统计量的期望",
    "weight": 0.85
  },
  {
    "source": "矩估计",
    "target": "估计量的方差",
    "weight": 0.8
  },
  {
    "source": "方差的性质",
    "target": "样本均值的方差",
    "weight": 0.9
  },
  {
    "source": "独立随机变量方差的性质",
    "target": "样本均值的方差",
    "weight": 0.9
  },
  {
    "source": "简单随机样本的性质",
    "target": "样本均值的方差",
    "weight": 0.9
  },
  {
    "source": "方差的定义",
    "target": "总体方差的计算",
    "weight": 0.9
  },
  {
    "source": "二阶原点矩",
    "target": "总体方差的计算",
    "weight": 0.9
  },
  {
    "source": "样本均值的方差",
    "target": "估计量的方差",
    "weight": 0.9
  },
  {
    "source": "连续型随机变量期望计算",
    "target": "方差计算公式",
    "weight": 0.9
  },
  {
    "source": "方差计算公式",
    "target": "总体方差计算",
    "weight": 0.95
  },
  {
    "source": "总体方差计算",
    "target": "样本均值的方差",
    "weight": 0.85
  },
  {
    "source": "方差的性质",
    "target": "估计量方差的计算",
    "weight": 0.9
  },
  {
    "source": "样本均值的方差",
    "target": "估计量方差的计算",
    "weight": 0.9
  },
  {
    "source": "三角换元法",
    "target": "定积分的计算",
    "weight": 0.9
  },
  {
    "source": "三角函数降幂公式",
    "target": "定积分的计算",
    "weight": 0.8
  },
  {
    "source": "圆的方程",
    "target": "定积分的几何意义",
    "weight": 0.9
  },
  {
    "source": "定积分的几何意义",
    "target": "定积分的计算",
    "weight": 0.85
  },
  {
    "source": "曲面法向量",
    "target": "空间曲线的切线方程",
    "weight": 0.85
  },
  {
    "source": "多元函数偏导数",
    "target": "曲面法向量",
    "weight": 0.9
  },
  {
    "source": "曲面法向量",
    "target": "曲面法线方程",
    "weight": 0.95
  },
  {
    "source": "一阶微分方程求解",
    "target": "二阶可降阶微分方程",
    "weight": 0.9
  },
  {
    "source": "第一类曲面积分",
    "target": "曲面积分的对称性",
    "weight": 0.85
  },
  {
    "source": "第一类曲面积分",
    "target": "第一类曲面积分的奇偶对称性",
    "weight": 0.9
  },
  {
    "source": "奇偶函数",
    "target": "第一类曲面积分的奇偶对称性",
    "weight": 0.85
  },
  {
    "source": "第一类曲面积分",
    "target": "第一类曲面积分的轮换对称性",
    "weight": 0.9
  },
  {
    "source": "轮换对称性",
    "target": "第一类曲面积分的轮换对称性",
    "weight": 0.85
  },
  {
    "source": "曲面的对称性",
    "target": "第一类曲面积分的奇偶对称性",
    "weight": 0.9
  },
  {
    "source": "奇偶函数的判定",
    "target": "第一类曲面积分的奇偶对称性",
    "weight": 0.9
  },
  {
    "source": "第一类曲面积分的奇偶对称性",
    "target": "第一类曲面积分的计算",
    "weight": 0.85
  },
  {
    "source": "数项级数收敛的定义",
    "target": "级数的线性性质",
    "weight": 0.85
  },
  {
    "source": "数项级数收敛的定义",
    "target": "级数收敛的必要条件",
    "weight": 0.9
  },
  {
    "source": "级数的线性性质",
    "target": "级数敛散性判断",
    "weight": 0.8
  },
  {
    "source": "级数收敛的概念",
    "target": "收敛级数的性质",
    "weight": 0.9
  },
  {
    "source": "收敛级数的性质",
    "target": "级数的线性运算",
    "weight": 0.85
  },
  {
    "source": "级数收敛的概念",
    "target": "级数平移的性质",
    "weight": 0.85
  },
  {
    "source": "级数平移的性质",
    "target": "级数的线性运算",
    "weight": 0.8
  },
  {
    "source": "交错级数",
    "target": "莱布尼茨判别法",
    "weight": 0.9
  },
  {
    "source": "反常积分敛散性",
    "target": "积分判别法",
    "weight": 0.9
  },
  {
    "source": "积分判别法",
    "target": "p级数推广的敛散性",
    "weight": 0.85
  },
  {
    "source": "p级数敛散性",
    "target": "交错级数敛散性",
    "weight": 0.8
  },
  {
    "source": "等价无穷小",
    "target": "比较审敛法的极限形式",
    "weight": 0.85
  },
  {
    "source": "比较审敛法的极限形式",
    "target": "级数发散判别",
    "weight": 0.9
  },
  {
    "source": "向量组的秩",
    "target": "线性相关与线性无关",
    "weight": 0.85
  },
  {
    "source": "线性相关与线性无关",
    "target": "向量组的线性表示",
    "weight": 0.9
  },
  {
    "source": "向量的线性无关",
    "target": "向量的线性表示",
    "weight": 0.85
  },
  {
    "source": "一阶线性非齐次微分方程",
    "target": "一阶线性非齐次微分方程通解公式",
    "weight": 0.95
  },
  {
    "source": "一阶线性非齐次微分方程通解公式",
    "target": "不定积分",
    "weight": 0.9
  },
  {
    "source": "函数极限",
    "target": "0比0型极限",
    "weight": 0.9
  },
  {
    "source": "数列极限",
    "target": "收敛半径",
    "weight": 0.85
  },
  {
    "source": "比值判别法",
    "target": "收敛半径",
    "weight": 0.9
  },
  {
    "source": "幂级数",
    "target": "收敛半径",
    "weight": 0.95
  },
  {
    "source": "幂级数",
    "target": "收敛区间",
    "weight": 0.95
  },
  {
    "source": "收敛半径",
    "target": "收敛区间",
    "weight": 0.95
  },
  {
    "source": "数列极限计算",
    "target": "幂级数比值法求收敛半径",
    "weight": 0.9
  },
  {
    "source": "幂级数比值法求收敛半径",
    "target": "收敛半径",
    "weight": 0.95
  },
  {
    "source": "调和级数发散",
    "target": "比较审敛法极限形式",
    "weight": 0.85
  },
  {
    "source": "比较审敛法极限形式",
    "target": "端点敛散性判断",
    "weight": 0.9
  },
  {
    "source": "数列极限",
    "target": "比较审敛法",
    "weight": 0.75
  },
  {
    "source": "等比级数收敛性",
    "target": "比较审敛法",
    "weight": 0.9
  },
  {
    "source": "交错级数审敛法",
    "target": "级数收敛性",
    "weight": 0.85
  },
  {
    "source": "比较审敛法",
    "target": "级数收敛性",
    "weight": 0.9
  },
  {
    "source": "级数收敛性",
    "target": "幂级数收敛域",
    "weight": 0.9
  },
  {
    "source": "坐标系建立",
    "target": "重心坐标计算",
    "weight": 0.9
  },
  {
    "source": "空间直角坐标系",
    "target": "球面方程",
    "weight": 0.9
  },
  {
    "source": "球面方程",
    "target": "三重积分的计算",
    "weight": 0.85
  },
  {
    "source": "三重积分",
    "target": "物体重心坐标",
    "weight": 0.95
  },
  {
    "source": "奇偶对称性",
    "target": "三重积分的计算",
    "weight": 0.85
  },
  {
    "source": "三重积分",
    "target": "三重积分的计算",
    "weight": 0.9
  },
  {
    "source": "奇偶对称性",
    "target": "三重积分计算",
    "weight": 0.9
  },
  {
    "source": "轮换对称性",
    "target": "三重积分计算",
    "weight": 0.9
  },
  {
    "source": "球体体积公式",
    "target": "三重积分计算",
    "weight": 0.85
  },
  {
    "source": "球面坐标系",
    "target": "三重积分计算",
    "weight": 0.95
  },
  {
    "source": "定积分计算",
    "target": "三重积分计算",
    "weight": 0.9
  },
  {
    "source": "牛顿-莱布尼茨公式",
    "target": "定积分计算",
    "weight": 0.95
  },
  {
    "source": "三重积分",
    "target": "三重积分的奇偶对称性",
    "weight": 0.9
  },
  {
    "source": "三重积分",
    "target": "三重积分的轮换对称性",
    "weight": 0.9
  },
  {
    "source": "三重积分的奇偶对称性",
    "target": "三重积分的轮换对称性",
    "weight": 0.7
  },
  {
    "source": "三重积分",
    "target": "球坐标系计算三重积分",
    "weight": 0.95
  },
  {
    "source": "三重积分的轮换对称性",
    "target": "球坐标系计算三重积分",
    "weight": 0.8
  },
  {
    "source": "三重积分",
    "target": "重心坐标的计算",
    "weight": 0.85
  },
  {
    "source": "球坐标系计算三重积分",
    "target": "重心坐标的计算",
    "weight": 0.8
  },
  {
    "source": "球面方程",
    "target": "三重积分",
    "weight": 0.85
  },
  {
    "source": "对称性",
    "target": "重心坐标",
    "weight": 0.9
  },
  {
    "source": "三重积分",
    "target": "重心坐标",
    "weight": 0.95
  },
  {
    "source": "球坐标变换",
    "target": "三重积分计算",
    "weight": 0.9
  },
  {
    "source": "三重积分的计算",
    "target": "球坐标系下的三重积分",
    "weight": 0.9
  },
  {
    "source": "三重积分的计算",
    "target": "重心的计算",
    "weight": 0.85
  },
  {
    "source": "连乘积",
    "target": "似然函数",
    "weight": 0.8
  },
  {
    "source": "似然函数",
    "target": "极大似然估计",
    "weight": 0.9
  },
  {
    "source": "似然函数",
    "target": "对数似然函数",
    "weight": 1.0
  },
  {
    "source": "对数似然函数",
    "target": "导数判断单调性",
    "weight": 0.85
  },
  {
    "source": "导数判断单调性",
    "target": "函数最值求解",
    "weight": 0.85
  },
  {
    "source": "函数最值求解",
    "target": "最大似然估计",
    "weight": 0.9
  },
  {
    "source": "似然函数",
    "target": "最大似然估计",
    "weight": 0.95
  },
  {
    "source": "共轭复根",
    "target": "特征方程",
    "weight": 0.85
  },
  {
    "source": "特征方程",
    "target": "二阶常系数线性齐次微分方程",
    "weight": 0.9
  },
  {
    "source": "特征根",
    "target": "微分方程的通解",
    "weight": 0.85
  },
  {
    "source": "一阶偏导数",
    "target": "梯度",
    "weight": 1.0
  },
  {
    "source": "偏导数",
    "target": "梯度",
    "weight": 0.95
  },
  {
    "source": "偏导数",
    "target": "散度",
    "weight": 0.9
  },
  {
    "source": "梯度",
    "target": "梯度的散度",
    "weight": 0.95
  },
  {
    "source": "散度",
    "target": "梯度的散度",
    "weight": 0.95
  },
  {
    "source": "连续偏导数",
    "target": "散度",
    "weight": 0.8
  },
  {
    "source": "方向余弦",
    "target": "单位法向量",
    "weight": 0.9
  },
  {
    "source": "单位法向量",
    "target": "斯托克斯公式",
    "weight": 0.85
  },
  {
    "source": "斯托克斯公式",
    "target": "空间曲线积分",
    "weight": 0.9
  },
  {
    "source": "雅可比行列式",
    "target": "第二类曲面积分",
    "weight": 0.8
  },
  {
    "source": "行列式展开",
    "target": "第二类曲面积分",
    "weight": 0.85
  },
  {
    "source": "第二类曲面积分",
    "target": "逐个投影法",
    "weight": 0.9
  },
  {
    "source": "逐个投影法",
    "target": "投影区域",
    "weight": 0.95
  },
  {
    "source": "绝对值不等式",
    "target": "投影区域",
    "weight": 0.75
  },
  {
    "source": "投影区域",
    "target": "二重积分计算",
    "weight": 0.9
  },
  {
    "source": "曲面的坐标面投影",
    "target": "第二类曲面积分",
    "weight": 0.85
  },
  {
    "source": "奇偶对称性",
    "target": "二重积分的计算",
    "weight": 0.9
  },
  {
    "source": "二重积分的计算",
    "target": "第二类曲面积分",
    "weight": 0.95
  },
  {
    "source": "空间曲线的方程",
    "target": "参数式法",
    "weight": 0.8
  },
  {
    "source": "独立同分布",
    "target": "随机变量的独立性",
    "weight": 0.9
  },
  {
    "source": "随机变量的独立性",
    "target": "独立随机变量期望的性质",
    "weight": 0.9
  },
  {
    "source": "独立随机变量期望的性质",
    "target": "期望的计算",
    "weight": 0.85
  },
  {
    "source": "期望的线性性质",
    "target": "期望的计算",
    "weight": 0.85
  },
  {
    "source": "样本均值",
    "target": "样本方差",
    "weight": 0.9
  },
  {
    "source": "样本方差",
    "target": "样本方差的期望",
    "weight": 0.95
  },
  {
    "source": "总体方差",
    "target": "样本方差的期望",
    "weight": 0.9
  },
  {
    "source": "数学期望的线性性质",
    "target": "样本方差的期望",
    "weight": 0.85
  },
  {
    "source": "随机变量的独立性",
    "target": "协方差的期望",
    "weight": 0.9
  },
  {
    "source": "极限",
    "target": "广义积分",
    "weight": 0.9
  },
  {
    "source": "定积分",
    "target": "广义积分",
    "weight": 0.9
  },
  {
    "source": "凑微分法",
    "target": "定积分计算",
    "weight": 0.9
  },
  {
    "source": "复合函数求导",
    "target": "隐函数求导",
    "weight": 0.95
  },
  {
    "source": "隐函数一阶导数",
    "target": "隐函数二阶导数",
    "weight": 1.0
  },
  {
    "source": "缺x型微分方程",
    "target": "变量代换",
    "weight": 0.9
  },
  {
    "source": "变量代换",
    "target": "分离变量法",
    "weight": 0.85
  },
  {
    "source": "分离变量法",
    "target": "微分方程通解",
    "weight": 0.9
  },
  {
    "source": "初始条件",
    "target": "特解",
    "weight": 0.95
  },
  {
    "source": "相似矩阵",
    "target": "矩阵的特征值",
    "weight": 0.9
  },
  {
    "source": "矩阵的特征值",
    "target": "特征值的定义",
    "weight": 0.9
  },
  {
    "source": "特征值的定义",
    "target": "行列式的计算",
    "weight": 0.85
  },
  {
    "source": "行列式的性质",
    "target": "特征值的计算",
    "weight": 0.9
  },
  {
    "source": "特征值",
    "target": "二次型化标准型",
    "weight": 0.85
  },
  {
    "source": "随机变量的分布函数",
    "target": "最大值随机变量的分布",
    "weight": 0.9
  },
  {
    "source": "高阶无穷小",
    "target": "洛必达法则",
    "weight": 0.8
  },
  {
    "source": "导数",
    "target": "佩亚诺余项泰勒公式",
    "weight": 0.9
  },
  {
    "source": "高阶无穷小",
    "target": "佩亚诺余项泰勒公式",
    "weight": 0.9
  },
  {
    "source": "佩亚诺余项泰勒公式",
    "target": "极限计算",
    "weight": 0.85
  },
  {
    "source": "随机变量的独立性",
    "target": "独立随机变量分布函数性质",
    "weight": 0.85
  },
  {
    "source": "分布函数",
    "target": "独立随机变量分布函数性质",
    "weight": 0.9
  },
  {
    "source": "极限的四则运算法则",
    "target": "导数的定义",
    "weight": 0.9
  },
  {
    "source": "导数的定义",
    "target": "利用导数定义求极限",
    "weight": 0.85
  },
  {
    "source": "极限的四则运算法则",
    "target": "待定系数法求极限",
    "weight": 0.8
  },
  {
    "source": "二元一次方程组求解",
    "target": "待定系数法求极限",
    "weight": 0.7
  },
  {
    "source": "向量组的线性表示",
    "target": "齐次线性方程组的解",
    "weight": 0.85
  },
  {
    "source": "齐次线性方程组的解",
    "target": "基础解系",
    "weight": 0.9
  },
  {
    "source": "基础解系",
    "target": "非齐次线性方程组的通解结构",
    "weight": 0.9
  },
  {
    "source": "非齐次线性方程组的特解",
    "target": "非齐次线性方程组的通解结构",
    "weight": 0.9
  },
  {
    "source": "向量的线性组合",
    "target": "线性非齐次方程组的矩阵表示",
    "weight": 0.9
  },
  {
    "source": "向量的线性表示",
    "target": "线性非齐次方程组求解",
    "weight": 0.85
  },
  {
    "source": "线性无关的定义",
    "target": "线性无关的判定",
    "weight": 0.9
  },
  {
    "source": "线性无关的判定",
    "target": "线性方程组的建立",
    "weight": 0.85
  },
  {
    "source": "线性方程组",
    "target": "系数矩阵",
    "weight": 0.95
  },
  {
    "source": "子式",
    "target": "矩阵的秩",
    "weight": 0.9
  },
  {
    "source": "矩阵的秩",
    "target": "齐次线性方程组的基础解系",
    "weight": 0.9
  },
  {
    "source": "矩阵的秩",
    "target": "自由未知量",
    "weight": 0.9
  },
  {
    "source": "线性无关",
    "target": "齐次线性方程组的基础解系",
    "weight": 0.85
  },
  {
    "source": "齐次线性方程组的基础解系",
    "target": "非齐次线性方程组的通解",
    "weight": 1.0
  },
  {
    "source": "可逆矩阵",
    "target": "相似矩阵",
    "weight": 0.9
  },
  {
    "source": "相似矩阵",
    "target": "特征多项式",
    "weight": 0.85
  },
  {
    "source": "行列式的乘法性质",
    "target": "特征多项式",
    "weight": 0.8
  },
  {
    "source": "特征多项式",
    "target": "特征值",
    "weight": 0.95
  },
  {
    "source": "实对称矩阵",
    "target": "相似对角化",
    "weight": 0.95
  },
  {
    "source": "特征值",
    "target": "相似对角化",
    "weight": 0.95
  },
  {
    "source": "相似对角化",
    "target": "矩阵相似",
    "weight": 0.8
  },
  {
    "source": "似然函数构造",
    "target": "对数似然函数",
    "weight": 0.95
  },
  {
    "source": "对数似然函数",
    "target": "导数运算",
    "weight": 0.9
  },
  {
    "source": "导数运算",
    "target": "极值必要条件",
    "weight": 0.9
  },
  {
    "source": "极值必要条件",
    "target": "极大似然估计值确定",
    "weight": 0.9
  },
  {
    "source": "指数对数转换",
    "target": "幂指函数极限",
    "weight": 0.9
  },
  {
    "source": "等价无穷小替换",
    "target": "幂指函数极限",
    "weight": 0.85
  },
  {
    "source": "常用等价无穷小公式",
    "target": "等价无穷小替换",
    "weight": 0.9
  },
  {
    "source": "偏导数",
    "target": "曲面法向量",
    "weight": 0.9
  },
  {
    "source": "曲面法向量",
    "target": "曲面切平面方程",
    "weight": 0.95
  },
  {
    "source": "平面法向量",
    "target": "曲面切平面方程",
    "weight": 0.85
  },
  {
    "source": "向量平行条件",
    "target": "曲面切平面方程",
    "weight": 0.8
  },
  {
    "source": "对数求导法",
    "target": "幂指函数求导",
    "weight": 0.9
  },
  {
    "source": "微积分基本定理",
    "target": "定积分计算",
    "weight": 0.9
  },
  {
    "source": "正态总体",
    "target": "样本均值分布",
    "weight": 0.9
  },
  {
    "source": "样本均值分布",
    "target": "标准化变换",
    "weight": 0.9
  },
  {
    "source": "标准化变换",
    "target": "标准正态分布",
    "weight": 0.95
  },
  {
    "source": "标准正态分布",
    "target": "上α分位点",
    "weight": 0.9
  },
  {
    "source": "上α分位点",
    "target": "方差已知时均值的置信区间",
    "weight": 0.95
  },
  {
    "source": "标准正态分布",
    "target": "标准正态分布分位点",
    "weight": 0.9
  },
  {
    "source": "标准正态分布分布函数",
    "target": "标准正态分布分位点",
    "weight": 0.9
  },
  {
    "source": "置信度",
    "target": "标准正态分布分位点",
    "weight": 0.85
  },
  {
    "source": "标准正态分布分位点",
    "target": "正态总体均值置信区间",
    "weight": 0.9
  },
  {
    "source": "样本均值",
    "target": "正态总体均值置信区间",
    "weight": 0.85
  },
  {
    "source": "定积分的计算",
    "target": "平面图形的面积",
    "weight": 0.9
  },
  {
    "source": "定积分的计算",
    "target": "旋转体的体积",
    "weight": 0.9
  },
  {
    "source": "常用函数的幂级数展开式",
    "target": "幂级数的间接展开法",
    "weight": 0.95
  },
  {
    "source": "导数",
    "target": "幂级数的间接展开法",
    "weight": 0.8
  },
  {
    "source": "定积分",
    "target": "幂级数的间接展开法",
    "weight": 0.8
  },
  {
    "source": "幂级数展开",
    "target": "逐项求导",
    "weight": 0.9
  },
  {
    "source": "幂级数展开",
    "target": "逐项积分",
    "weight": 0.9
  },
  {
    "source": "逐项求导",
    "target": "收敛区间",
    "weight": 0.8
  },
  {
    "source": "逐项积分",
    "target": "收敛区间",
    "weight": 0.8
  },
  {
    "source": "收敛区间",
    "target": "收敛端点",
    "weight": 0.85
  },
  {
    "source": "收敛端点",
    "target": "函数连续性",
    "weight": 0.85
  },
  {
    "source": "证明不等式",
    "target": "作差法",
    "weight": 0.75
  },
  {
    "source": "变限积分求导",
    "target": "函数单调性判定",
    "weight": 0.9
  },
  {
    "source": "函数单调性判定",
    "target": "积分不等式证明",
    "weight": 0.9
  },
  {
    "source": "变限积分求导",
    "target": "积分不等式证明",
    "weight": 0.85
  },
  {
    "source": "逆矩阵",
    "target": "矩阵相似",
    "weight": 0.85
  },
  {
    "source": "伴随矩阵",
    "target": "矩阵相似",
    "weight": 0.85
  },
  {
    "source": "矩阵相似",
    "target": "特征值与特征向量",
    "weight": 0.9
  },
  {
    "source": "特征值",
    "target": "特征向量",
    "weight": 0.95
  },
  {
    "source": "矩阵运算",
    "target": "矩阵的特征值",
    "weight": 0.85
  },
  {
    "source": "齐次线性方程组求解",
    "target": "特征向量求解",
    "weight": 0.95
  },
  {
    "source": "线性无关",
    "target": "基础解系",
    "weight": 0.95
  },
  {
    "source": "基础解系",
    "target": "特征向量的线性组合",
    "weight": 0.85
  },
  {
    "source": "特征值与特征向量的定义",
    "target": "伴随矩阵的特征值与特征向量",
    "weight": 0.9
  },
  {
    "source": "伴随矩阵的性质",
    "target": "伴随矩阵的特征值与特征向量",
    "weight": 0.9
  },
  {
    "source": "特征值与特征向量的定义",
    "target": "相似矩阵的特征值与特征向量",
    "weight": 0.9
  },
  {
    "source": "伴随矩阵的特征值与特征向量",
    "target": "相似矩阵的特征值与特征向量",
    "weight": 0.85
  },
  {
    "source": "特征值与特征向量的定义",
    "target": "矩阵多项式的特征值",
    "weight": 0.85
  },
  {
    "source": "相似矩阵的特征值与特征向量",
    "target": "矩阵多项式的特征值",
    "weight": 0.85
  },
  {
    "source": "行列式的性质",
    "target": "矩阵可逆的判定",
    "weight": 0.8
  },
  {
    "source": "矩阵可逆的判定",
    "target": "伴随矩阵的特征值与特征向量",
    "weight": 0.75
  },
  {
    "source": "特征值与特征向量的定义",
    "target": "特征多项式",
    "weight": 0.85
  },
  {
    "source": "线性无关",
    "target": "特征向量",
    "weight": 0.8
  },
  {
    "source": "行列式的计算",
    "target": "矩阵的秩",
    "weight": 0.85
  },
  {
    "source": "行列式为零",
    "target": "矩阵的秩",
    "weight": 0.9
  },
  {
    "source": "二阶行列式计算",
    "target": "矩阵的秩",
    "weight": 0.85
  },
  {
    "source": "矩阵的秩",
    "target": "系数矩阵与增广矩阵的秩",
    "weight": 0.9
  },
  {
    "source": "系数矩阵与增广矩阵的秩",
    "target": "线性方程组解的判定",
    "weight": 0.95
  },
  {
    "source": "齐次线性方程组非零解",
    "target": "行列式为零",
    "weight": 0.95
  },
  {
    "source": "三阶行列式计算",
    "target": "行列式为零",
    "weight": 0.85
  },
  {
    "source": "线性方程组解的判定",
    "target": "线性方程组的几何意义",
    "weight": 0.85
  },
  {
    "source": "线性方程组解的判定",
    "target": "充要条件",
    "weight": 0.75
  },
  {
    "source": "线性方程组",
    "target": "克莱姆法则",
    "weight": 0.85
  },
  {
    "source": "行列式计算",
    "target": "线性方程组解的判定",
    "weight": 0.9
  },
  {
    "source": "矩阵的秩",
    "target": "线性方程组解的判定",
    "weight": 0.95
  },
  {
    "source": "方程组的初等变换",
    "target": "同解方程组",
    "weight": 0.9
  },
  {
    "source": "已知条件代入化简",
    "target": "同解方程组",
    "weight": 0.8
  },
  {
    "source": "导数的几何意义",
    "target": "切线方程",
    "weight": 0.95
  },
  {
    "source": "对数函数求导",
    "target": "导数的几何意义",
    "weight": 0.8
  },
  {
    "source": "复合函数求导",
    "target": "不定积分",
    "weight": 0.9
  },
  {
    "source": "原函数概念",
    "target": "不定积分",
    "weight": 0.9
  },
  {
    "source": "第二类曲线积分",
    "target": "格林公式",
    "weight": 0.9
  },
  {
    "source": "欧拉方程",
    "target": "变量代换法",
    "weight": 0.9
  },
  {
    "source": "变量代换法",
    "target": "常系数线性微分方程",
    "weight": 0.85
  },
  {
    "source": "伴随矩阵性质",
    "target": "矩阵方程求解",
    "weight": 0.85
  },
  {
    "source": "矩阵行列式性质",
    "target": "矩阵方程求解",
    "weight": 0.8
  },
  {
    "source": "指数分布",
    "target": "方差计算",
    "weight": 0.85
  },
  {
    "source": "方差计算",
    "target": "概率计算",
    "weight": 0.8
  },
  {
    "source": "极限概念",
    "target": "无穷小量",
    "weight": 0.9
  },
  {
    "source": "无穷小量",
    "target": "高阶无穷小",
    "weight": 0.9
  },
  {
    "source": "泰勒展开",
    "target": "高阶无穷小",
    "weight": 0.85
  },
  {
    "source": "定积分的性质",
    "target": "无穷小量比较",
    "weight": 0.75
  },
  {
    "source": "导数定义",
    "target": "极限的保号性",
    "weight": 0.95
  },
  {
    "source": "极限的保号性",
    "target": "函数局部的性质",
    "weight": 0.8
  },
  {
    "source": "级数收敛必要条件",
    "target": "正项级数判别法",
    "weight": 0.85
  },
  {
    "source": "数列极限",
    "target": "级数收敛的必要条件",
    "weight": 0.9
  },
  {
    "source": "级数收敛的必要条件",
    "target": "级数敛散性",
    "weight": 0.95
  },
  {
    "source": "连续函数性质",
    "target": "变限积分求导",
    "weight": 0.85
  },
  {
    "source": "交换积分次序",
    "target": "变限积分求导",
    "weight": 0.9
  },
  {
    "source": "变限积分求导",
    "target": "二阶导数",
    "weight": 0.85
  },
  {
    "source": "矩阵乘法",
    "target": "初等列变换",
    "weight": 0.9
  },
  {
    "source": "初等列变换",
    "target": "初等矩阵",
    "weight": 0.9
  },
  {
    "source": "初等矩阵",
    "target": "可逆矩阵",
    "weight": 0.85
  },
  {
    "source": "矩阵乘法",
    "target": "矩阵乘积为零矩阵",
    "weight": 0.8
  },
  {
    "source": "矩阵乘积为零矩阵",
    "target": "齐次线性方程组的解",
    "weight": 0.9
  },
  {
    "source": "齐次线性方程组的解",
    "target": "线性相关",
    "weight": 0.95
  },
  {
    "source": "随机变量",
    "target": "正态分布",
    "weight": 0.9
  },
  {
    "source": "正态分布",
    "target": "标准正态分布",
    "weight": 0.9
  },
  {
    "source": "标准正态分布",
    "target": "分位数",
    "weight": 0.85
  },
  {
    "source": "标准正态分布",
    "target": "概率计算",
    "weight": 0.9
  },
  {
    "source": "随机变量",
    "target": "方差",
    "weight": 0.9
  },
  {
    "source": "方差",
    "target": "协方差",
    "weight": 0.85
  },
  {
    "source": "随机变量",
    "target": "独立同分布",
    "weight": 0.8
  },
  {
    "source": "随机变量",
    "target": "样本均值",
    "weight": 0.8
  },
  {
    "source": "方差",
    "target": "样本均值",
    "weight": 0.75
  },
  {
    "source": "协方差",
    "target": "样本均值",
    "weight": 0.7
  },
  {
    "source": "线性方程组",
    "target": "齐次线性方程组",
    "weight": 0.9
  },
  {
    "source": "齐次线性方程组",
    "target": "非零解",
    "weight": 0.85
  },
  {
    "source": "齐次线性方程组",
    "target": "通解",
    "weight": 0.9
  },
  {
    "source": "特征方程",
    "target": "特征值",
    "weight": 0.9
  },
  {
    "source": "条件概率",
    "target": "联合概率分布",
    "weight": 0.85
  },
  {
    "source": "联合概率分布",
    "target": "边缘分布",
    "weight": 0.9
  },
  {
    "source": "联合概率分布",
    "target": "协方差",
    "weight": 0.8
  },
  {
    "source": "边缘分布",
    "target": "数学期望",
    "weight": 0.85
  },
  {
    "source": "数学期望",
    "target": "方差",
    "weight": 1.0
  },
  {
    "source": "协方差",
    "target": "相关系数",
    "weight": 0.95
  },
  {
    "source": "方差",
    "target": "相关系数",
    "weight": 0.9
  },
  {
    "source": "分布函数",
    "target": "概率密度函数",
    "weight": 0.95
  },
  {
    "source": "概率密度函数",
    "target": "矩估计",
    "weight": 0.85
  },
  {
    "source": "概率密度函数",
    "target": "最大似然估计",
    "weight": 0.9
  },
  {
    "source": "直线斜率",
    "target": "两直线垂直的条件",
    "weight": 0.9
  },
  {
    "source": "对数函数求导公式",
    "target": "曲线的切线方程",
    "weight": 0.9
  },
  {
    "source": "导数与微分的概念",
    "target": "不定积分的概念",
    "weight": 0.9
  },
  {
    "source": "换元积分法",
    "target": "凑微分法",
    "weight": 0.85
  },
  {
    "source": "导数概念与计算",
    "target": "不定积分",
    "weight": 0.9
  },
  {
    "source": "不定积分",
    "target": "利用初始条件求特解",
    "weight": 0.85
  },
  {
    "source": "极坐标系",
    "target": "曲线积分",
    "weight": 0.85
  },
  {
    "source": "曲线积分",
    "target": "定积分",
    "weight": 0.9
  },
  {
    "source": "随机变量的独立性",
    "target": "协方差性质",
    "weight": 0.9
  },
  {
    "source": "协方差性质",
    "target": "协方差的计算",
    "weight": 0.85
  },
  {
    "source": "样本均值",
    "target": "协方差的计算",
    "weight": 0.8
  },
  {
    "source": "协方差的计算",
    "target": "方差的计算",
    "weight": 0.9
  },
  {
    "source": "随机变量的独立性",
    "target": "独立和的方差",
    "weight": 0.9
  },
  {
    "source": "独立和的方差",
    "target": "方差计算",
    "weight": 0.85
  },
  {
    "source": "拉格朗日中值定理条件",
    "target": "拉格朗日中值定理",
    "weight": 0.9
  },
  {
    "source": "拉格朗日中值定理",
    "target": "不等式证明",
    "weight": 0.85
  },
  {
    "source": "导数判断单调性",
    "target": "函数单调性",
    "weight": 0.95
  },
  {
    "source": "牛顿第二定律",
    "target": "微分方程建模",
    "weight": 0.9
  },
  {
    "source": "微分方程建模",
    "target": "可分离变量微分方程",
    "weight": 0.85
  },
  {
    "source": "可分离变量微分方程",
    "target": "不定积分",
    "weight": 0.9
  },
  {
    "source": "不定积分",
    "target": "初始条件求特解",
    "weight": 0.85
  },
  {
    "source": "初始条件求特解",
    "target": "定积分的应用",
    "weight": 0.8
  },
  {
    "source": "定积分的应用",
    "target": "反常积分",
    "weight": 0.9
  },
  {
    "source": "定积分的应用",
    "target": "极限计算",
    "weight": 0.8
  },
  {
    "source": "微分方程建模",
    "target": "二阶微分方程",
    "weight": 0.85
  },
  {
    "source": "二阶微分方程",
    "target": "可降阶的高阶微分方程",
    "weight": 0.9
  },
  {
    "source": "二阶常系数齐次线性微分方程",
    "target": "特征方程法",
    "weight": 0.9
  },
  {
    "source": "特征方程法",
    "target": "微分方程通解",
    "weight": 0.85
  },
  {
    "source": "微分方程通解",
    "target": "初值问题求特解",
    "weight": 0.9
  },
  {
    "source": "极限计算",
    "target": "无穷远极限求解",
    "weight": 0.8
  },
  {
    "source": "高斯公式",
    "target": "第二类曲面积分计算",
    "weight": 0.95
  },
  {
    "source": "补面法",
    "target": "高斯公式应用",
    "weight": 0.9
  },
  {
    "source": "一阶偏导数",
    "target": "驻点",
    "weight": 0.9
  },
  {
    "source": "驻点",
    "target": "极值点存在的充分条件",
    "weight": 0.9
  },
  {
    "source": "一阶偏导数",
    "target": "二阶偏导数",
    "weight": 1.0
  },
  {
    "source": "二阶偏导数",
    "target": "极值点存在的充分条件",
    "weight": 0.95
  },
  {
    "source": "隐函数求导法",
    "target": "一阶偏导数",
    "weight": 0.85
  },
  {
    "source": "隐函数求导法",
    "target": "二阶偏导数",
    "weight": 0.9
  },
  {
    "source": "偏导数概念",
    "target": "隐函数求导法",
    "weight": 0.85
  },
  {
    "source": "二阶偏导数",
    "target": "二元函数极值的充分条件",
    "weight": 0.95
  },
  {
    "source": "二元函数极值的充分条件",
    "target": "极小值点",
    "weight": 0.9
  },
  {
    "source": "偏导数",
    "target": "多元函数极值的判别",
    "weight": 0.9
  },
  {
    "source": "多元函数极值的判别",
    "target": "极大值",
    "weight": 0.85
  },
  {
    "source": "自由未知量",
    "target": "基础解系",
    "weight": 0.95
  },
  {
    "source": "基础解系",
    "target": "通解",
    "weight": 0.95
  },
  {
    "source": "矩阵的初等行变换",
    "target": "同解方程组",
    "weight": 0.9
  },
  {
    "source": "同解方程组",
    "target": "基础解系",
    "weight": 0.9
  },
  {
    "source": "基础解系",
    "target": "齐次线性方程组通解",
    "weight": 0.95
  },
  {
    "source": "齐次线性方程组的基础解系",
    "target": "齐次线性方程组的通解",
    "weight": 0.95
  },
  {
    "source": "行列式的计算",
    "target": "特征多项式",
    "weight": 0.85
  },
  {
    "source": "特征多项式",
    "target": "矩阵的特征值",
    "weight": 0.9
  },
  {
    "source": "极限",
    "target": "斜渐近线",
    "weight": 0.9
  },
  {
    "source": "不定积分",
    "target": "一阶线性微分方程",
    "weight": 0.85
  },
  {
    "source": "一阶线性微分方程",
    "target": "微分方程初值问题",
    "weight": 0.8
  },
  {
    "source": "梯度",
    "target": "方向导数",
    "weight": 0.95
  },
  {
    "source": "第二类曲面积分",
    "target": "高斯公式",
    "weight": 0.9
  },
  {
    "source": "高斯公式",
    "target": "三重积分",
    "weight": 0.95
  },
  {
    "source": "向量与矩阵的表示",
    "target": "矩阵乘法",
    "weight": 0.8
  },
  {
    "source": "矩阵乘法",
    "target": "行列式的乘积法则",
    "weight": 0.9
  },
  {
    "source": "范德蒙德行列式",
    "target": "行列式的计算",
    "weight": 0.9
  },
  {
    "source": "条件概率",
    "target": "全概率公式",
    "weight": 0.9
  },
  {
    "source": "离散型随机变量",
    "target": "全概率公式",
    "weight": 0.8
  },
  {
    "source": "数列极限",
    "target": "分段函数",
    "weight": 0.75
  },
  {
    "source": "分段函数",
    "target": "函数可导性",
    "weight": 0.85
  },
  {
    "source": "连续性",
    "target": "函数可导性",
    "weight": 0.85
  },
  {
    "source": "连续函数",
    "target": "原函数",
    "weight": 0.85
  },
  {
    "source": "奇函数与偶函数",
    "target": "原函数的奇偶性",
    "weight": 0.9
  },
  {
    "source": "原函数",
    "target": "变限积分",
    "weight": 0.85
  },
  {
    "source": "一阶导数",
    "target": "二阶导数",
    "weight": 0.95
  },
  {
    "source": "偏导数",
    "target": "二阶偏导数",
    "weight": 0.95
  },
  {
    "source": "偏导数",
    "target": "混合偏导数",
    "weight": 0.9
  },
  {
    "source": "二阶偏导数",
    "target": "偏微分方程",
    "weight": 0.8
  },
  {
    "source": "偏导数",
    "target": "隐函数存在定理",
    "weight": 0.9
  },
  {
    "source": "偏导数",
    "target": "连续偏导数",
    "weight": 0.85
  },
  {
    "source": "隐函数存在定理",
    "target": "隐函数",
    "weight": 0.95
  },
  {
    "source": "特征值与特征向量的定义",
    "target": "向量线性相关性判定",
    "weight": 0.9
  },
  {
    "source": "不同特征值对应的特征向量线性无关",
    "target": "向量线性相关性判定",
    "weight": 0.85
  },
  {
    "source": "初等矩阵与初等变换",
    "target": "伴随矩阵的性质",
    "weight": 0.9
  },
  {
    "source": "逆矩阵的性质",
    "target": "伴随矩阵的性质",
    "weight": 0.85
  },
  {
    "source": "概率的基本性质",
    "target": "二维离散型随机变量联合分布",
    "weight": 0.8
  },
  {
    "source": "事件的独立性",
    "target": "二维离散型随机变量",
    "weight": 0.85
  },
  {
    "source": "一阶线性微分方程",
    "target": "一阶线性微分方程求解公式",
    "weight": 0.9
  },
  {
    "source": "一阶线性微分方程的标准形式",
    "target": "一阶线性微分方程的通解公式",
    "weight": 0.9
  },
  {
    "source": "不定积分的计算",
    "target": "一阶线性微分方程的通解公式",
    "weight": 0.85
  },
  {
    "source": "一阶线性微分方程的通解公式",
    "target": "一阶线性微分方程的特解",
    "weight": 0.9
  },
  {
    "source": "一阶偏导数",
    "target": "方向导数的计算",
    "weight": 0.95
  },
  {
    "source": "方向余弦",
    "target": "方向导数的计算",
    "weight": 0.9
  },
  {
    "source": "偏导数",
    "target": "方向导数",
    "weight": 0.95
  },
  {
    "source": "方向余弦",
    "target": "方向导数",
    "weight": 0.9
  },
  {
    "source": "一阶连续偏导数",
    "target": "高斯公式",
    "weight": 0.9
  },
  {
    "source": "三重积分",
    "target": "高斯公式",
    "weight": 0.85
  },
  {
    "source": "三重积分",
    "target": "球面坐标",
    "weight": 0.9
  },
  {
    "source": "向量的线性组合",
    "target": "矩阵的乘法",
    "weight": 0.9
  },
  {
    "source": "矩阵的乘法",
    "target": "行列式的性质",
    "weight": 0.95
  },
  {
    "source": "数列极限",
    "target": "夹逼准则",
    "weight": 0.9
  },
  {
    "source": "极限",
    "target": "导数定义",
    "weight": 0.95
  },
  {
    "source": "导数定义",
    "target": "不可导点",
    "weight": 0.85
  },
  {
    "source": "夹逼准则",
    "target": "求函数表达式",
    "weight": 0.7
  },
  {
    "source": "奇偶性定义",
    "target": "函数奇偶性判定",
    "weight": 0.9
  },
  {
    "source": "原函数概念",
    "target": "原函数表示",
    "weight": 0.9
  },
  {
    "source": "定积分概念",
    "target": "原函数表示",
    "weight": 0.95
  },
  {
    "source": "导数概念",
    "target": "奇偶函数求导性质",
    "weight": 0.85
  },
  {
    "source": "奇偶性定义",
    "target": "奇偶函数求导性质",
    "weight": 0.9
  },
  {
    "source": "奇偶函数求导性质",
    "target": "原函数与被积函数奇偶性关系",
    "weight": 0.95
  },
  {
    "source": "偏导数概念",
    "target": "偏导数计算",
    "weight": 0.9
  },
  {
    "source": "复合函数求导法则",
    "target": "偏导数计算",
    "weight": 0.95
  },
  {
    "source": "多元复合函数求导法则",
    "target": "二阶偏导数计算",
    "weight": 0.9
  },
  {
    "source": "一阶偏导数",
    "target": "二阶偏导数计算",
    "weight": 0.95
  },
  {
    "source": "二阶偏导数计算",
    "target": "偏导数恒等式验证",
    "weight": 0.85
  },
  {
    "source": "连续偏导数",
    "target": "隐函数存在定理",
    "weight": 0.9
  },
  {
    "source": "隐函数存在定理",
    "target": "隐函数求导公式",
    "weight": 0.95
  },
  {
    "source": "多元函数偏导数",
    "target": "隐函数存在定理",
    "weight": 0.9
  },
  {
    "source": "特征值与特征向量的定义",
    "target": "向量线性无关",
    "weight": 0.85
  },
  {
    "source": "特征值与特征向量的定义",
    "target": "不同特征值对应的特征向量线性无关",
    "weight": 0.9
  },
  {
    "source": "不同特征值对应的特征向量线性无关",
    "target": "齐次线性方程组的建立",
    "weight": 0.85
  },
  {
    "source": "齐次线性方程组解的判定",
    "target": "向量组的线性无关证明",
    "weight": 0.9
  },
  {
    "source": "线性相关与线性无关的定义",
    "target": "向量组的线性相关性判定",
    "weight": 0.85
  },
  {
    "source": "特征值与特征向量的定义",
    "target": "向量组的矩阵表示",
    "weight": 0.8
  },
  {
    "source": "特征值与特征向量定义",
    "target": "不同特征值对应特征向量的线性无关性",
    "weight": 0.9
  },
  {
    "source": "向量组线性相关性与矩阵的秩",
    "target": "矩阵乘积的秩不等式",
    "weight": 0.85
  },
  {
    "source": "不同特征值对应特征向量的线性无关性",
    "target": "矩阵乘积的秩不等式",
    "weight": 0.8
  },
  {
    "source": "矩阵的秩",
    "target": "矩阵可逆",
    "weight": 0.9
  },
  {
    "source": "矩阵可逆",
    "target": "矩阵的行列式",
    "weight": 0.95
  },
  {
    "source": "矩阵可逆",
    "target": "齐次线性方程组",
    "weight": 0.85
  },
  {
    "source": "特征值与特征向量",
    "target": "线性无关",
    "weight": 0.9
  },
  {
    "source": "特征值与特征向量",
    "target": "线性表出",
    "weight": 0.85
  },
  {
    "source": "矩阵乘法的线性性",
    "target": "线性表出",
    "weight": 0.8
  },
  {
    "source": "线性表出",
    "target": "等价向量组",
    "weight": 0.95
  },
  {
    "source": "等价向量组",
    "target": "向量组的秩",
    "weight": 0.9
  },
  {
    "source": "单位矩阵",
    "target": "初等矩阵",
    "weight": 0.9
  },
  {
    "source": "初等矩阵",
    "target": "初等行变换",
    "weight": 0.85
  },
  {
    "source": "行列式的性质",
    "target": "初等矩阵的行列式",
    "weight": 0.8
  },
  {
    "source": "伴随矩阵",
    "target": "逆矩阵",
    "weight": 0.95
  },
  {
    "source": "逆矩阵",
    "target": "矩阵乘积的逆",
    "weight": 0.9
  },
  {
    "source": "伴随矩阵",
    "target": "矩阵乘积的伴随",
    "weight": 0.9
  },
  {
    "source": "行列式",
    "target": "行列式的乘法",
    "weight": 0.85
  },
  {
    "source": "正态分布",
    "target": "正态分布标准化",
    "weight": 0.9
  },
  {
    "source": "标准正态分布",
    "target": "卡方分布",
    "weight": 0.95
  },
  {
    "source": "正态分布",
    "target": "正态分布的标准化",
    "weight": 0.9
  },
  {
    "source": "正态分布",
    "target": "卡方分布",
    "weight": 0.85
  },
  {
    "source": "正态分布的标准化",
    "target": "t分布",
    "weight": 0.85
  },
  {
    "source": "卡方分布",
    "target": "t分布",
    "weight": 0.8
  },
  {
    "source": "卡方分布",
    "target": "F分布",
    "weight": 0.9
  },
  {
    "source": "取整函数",
    "target": "二重积分对区域的可加性",
    "weight": 0.85
  },
  {
    "source": "二重积分对区域的可加性",
    "target": "极坐标化累次积分",
    "weight": 0.9
  },
  {
    "source": "极坐标化累次积分",
    "target": "牛顿-莱布尼茨公式",
    "weight": 0.95
  },
  {
    "source": "极坐标变换",
    "target": "二重积分计算",
    "weight": 0.9
  },
  {
    "source": "定积分计算",
    "target": "二重积分计算",
    "weight": 0.95
  },
  {
    "source": "凑微分法",
    "target": "牛顿-莱布尼茨公式",
    "weight": 0.85
  },
  {
    "source": "二重积分的极坐标换元法",
    "target": "取整函数的处理",
    "weight": 0.8
  },
  {
    "source": "取整函数的处理",
    "target": "定积分对区间的可加性",
    "weight": 0.85
  },
  {
    "source": "定积分对区间的可加性",
    "target": "定积分的计算",
    "weight": 0.9
  },
  {
    "source": "牛顿-莱布尼茨公式",
    "target": "定积分的计算",
    "weight": 1.0
  },
  {
    "source": "比值判别法",
    "target": "幂级数收敛半径",
    "weight": 0.95
  },
  {
    "source": "幂级数收敛半径",
    "target": "幂级数收敛区间",
    "weight": 0.95
  },
  {
    "source": "等比级数求和公式",
    "target": "幂级数求和",
    "weight": 0.85
  },
  {
    "source": "幂级数逐项求导",
    "target": "幂级数求和",
    "weight": 0.9
  },
  {
    "source": "分部积分法",
    "target": "定积分计算",
    "weight": 0.9
  },
  {
    "source": "偏导数计算",
    "target": "曲线积分与路径无关",
    "weight": 0.9
  },
  {
    "source": "常微分方程求解",
    "target": "曲线积分与路径无关",
    "weight": 0.85
  },
  {
    "source": "行列式计算",
    "target": "矩阵的秩",
    "weight": 0.8
  },
  {
    "source": "特征方程",
    "target": "特征值与特征向量",
    "weight": 0.95
  },
  {
    "source": "齐次线性方程组基础解系",
    "target": "特征向量求解",
    "weight": 0.9
  },
  {
    "source": "特征值与特征向量",
    "target": "正交变换化二次型为标准形",
    "weight": 0.9
  },
  {
    "source": "施密特正交化",
    "target": "正交变换化二次型为标准形",
    "weight": 0.85
  },
  {
    "source": "随机变量的独立性",
    "target": "协方差计算",
    "weight": 0.9
  },
  {
    "source": "数学期望的性质",
    "target": "协方差计算",
    "weight": 0.85
  },
  {
    "source": "可分离变量的微分方程",
    "target": "一阶微分方程求解",
    "weight": 0.9
  },
  {
    "source": "空间解析几何",
    "target": "点到平面的距离",
    "weight": 0.85
  },
  {
    "source": "逆矩阵",
    "target": "矩阵方程求解",
    "weight": 0.9
  },
  {
    "source": "矩阵的运算",
    "target": "矩阵方程求解",
    "weight": 0.9
  },
  {
    "source": "行列式的性质",
    "target": "行列式的计算",
    "weight": 0.9
  },
  {
    "source": "随机变量的独立性",
    "target": "多维随机变量函数的分布",
    "weight": 0.85
  },
  {
    "source": "均匀分布",
    "target": "多维随机变量函数的分布",
    "weight": 0.8
  },
  {
    "source": "微分定义",
    "target": "增量与微分的关系",
    "weight": 0.9
  },
  {
    "source": "二阶导数",
    "target": "函数的凹凸性",
    "weight": 0.95
  },
  {
    "source": "函数的凹凸性",
    "target": "函数增量与微分的比较",
    "weight": 0.9
  },
  {
    "source": "二重积分的概念",
    "target": "极坐标下的二重积分",
    "weight": 0.9
  },
  {
    "source": "极坐标下的二重积分",
    "target": "二重积分的坐标转换",
    "weight": 0.9
  },
  {
    "source": "二重积分的坐标转换",
    "target": "直角坐标下的二重积分",
    "weight": 0.9
  },
  {
    "source": "数项级数收敛",
    "target": "绝对收敛",
    "weight": 0.9
  },
  {
    "source": "矩阵的秩",
    "target": "非齐次线性方程组求解",
    "weight": 0.9
  },
  {
    "source": "线性无关",
    "target": "非齐次线性方程组解的结构",
    "weight": 0.85
  },
  {
    "source": "非齐次线性方程组解的结构",
    "target": "非齐次线性方程组通解",
    "weight": 0.95
  },
  {
    "source": "特征值与特征向量",
    "target": "实对称矩阵对角化",
    "weight": 0.95
  },
  {
    "source": "正交矩阵",
    "target": "实对称矩阵对角化",
    "weight": 0.9
  },
  {
    "source": "概率密度",
    "target": "随机变量函数的分布",
    "weight": 0.9
  },
  {
    "source": "随机变量函数的分布",
    "target": "二维随机变量分布函数",
    "weight": 0.8
  },
  {
    "source": "概率密度",
    "target": "最大似然估计",
    "weight": 0.9
  },
  {
    "source": "简单随机样本",
    "target": "最大似然估计",
    "weight": 0.85
  },
  {
    "source": "等价无穷小替换",
    "target": "极限计算",
    "weight": 0.9
  },
  {
    "source": "分离变量法",
    "target": "微分方程求解",
    "weight": 0.95
  },
  {
    "source": "补面法",
    "target": "高斯公式",
    "weight": 0.9
  },
  {
    "source": "高斯公式",
    "target": "曲面积分计算",
    "weight": 0.95
  },
  {
    "source": "散度计算",
    "target": "高斯公式",
    "weight": 0.85
  },
  {
    "source": "空间立体体积",
    "target": "三重积分计算",
    "weight": 0.8
  },
  {
    "source": "对数运算",
    "target": "微分方程求解",
    "weight": 0.7
  },
  {
    "source": "高斯公式",
    "target": "三重积分计算",
    "weight": 0.9
  },
  {
    "source": "平行截面法求体积",
    "target": "定积分计算",
    "weight": 0.9
  },
  {
    "source": "定积分计算",
    "target": "体积计算",
    "weight": 0.9
  },
  {
    "source": "球面坐标变换",
    "target": "三重积分计算",
    "weight": 0.85
  },
  {
    "source": "球面坐标系",
    "target": "三重积分的计算",
    "weight": 0.9
  },
  {
    "source": "柱面坐标系",
    "target": "三重积分的计算",
    "weight": 0.9
  },
  {
    "source": "定积分的计算",
    "target": "三重积分的计算",
    "weight": 0.85
  },
  {
    "source": "平面的一般方程",
    "target": "点到平面的距离",
    "weight": 0.85
  },
  {
    "source": "矩阵的乘法",
    "target": "矩阵方程求解",
    "weight": 0.8
  },
  {
    "source": "矩阵方程求解",
    "target": "抽象行列式的计算",
    "weight": 0.85
  },
  {
    "source": "行列式的性质",
    "target": "矩阵方程的行列式计算",
    "weight": 0.9
  },
  {
    "source": "事件独立性",
    "target": "乘法公式",
    "weight": 0.85
  },
  {
    "source": "齐次方程的解",
    "target": "基础解系",
    "weight": 0.9
  },
  {
    "source": "非齐次方程的解",
    "target": "齐次方程的解",
    "weight": 0.85
  },
  {
    "source": "基础解系",
    "target": "矩阵的秩",
    "weight": 0.9
  },
  {
    "source": "初等行变换",
    "target": "矩阵的秩",
    "weight": 0.85
  },
  {
    "source": "系数矩阵",
    "target": "增广矩阵",
    "weight": 0.8
  },
  {
    "source": "矩阵的初等行变换",
    "target": "矩阵的秩",
    "weight": 0.9
  },
  {
    "source": "矩阵的初等行变换",
    "target": "行最简形矩阵",
    "weight": 0.9
  },
  {
    "source": "行最简形矩阵",
    "target": "齐次线性方程组的基础解系",
    "weight": 0.85
  },
  {
    "source": "行最简形矩阵",
    "target": "非齐次线性方程组的特解",
    "weight": 0.85
  },
  {
    "source": "非齐次线性方程组的特解",
    "target": "非齐次线性方程组的通解",
    "weight": 1.0
  },
  {
    "source": "数学期望",
    "target": "矩估计法",
    "weight": 0.95
  },
  {
    "source": "样本均值",
    "target": "矩估计法",
    "weight": 0.9
  },
  {
    "source": "对数似然函数",
    "target": "导数求极值",
    "weight": 0.85
  },
  {
    "source": "导数求极值",
    "target": "最大似然估计",
    "weight": 0.95
  },
  {
    "source": "极限概念",
    "target": "等价无穷小",
    "weight": 0.9
  },
  {
    "source": "泰勒公式",
    "target": "等价无穷小替换",
    "weight": 0.9
  },
  {
    "source": "极限计算",
    "target": "函数渐近线",
    "weight": 0.85
  },
  {
    "source": "函数渐近线",
    "target": "水平渐近线",
    "weight": 0.9
  },
  {
    "source": "函数渐近线",
    "target": "垂直渐近线",
    "weight": 0.9
  },
  {
    "source": "函数渐近线",
    "target": "斜渐近线",
    "weight": 0.9
  },
  {
    "source": "定积分概念",
    "target": "定积分的几何意义",
    "weight": 0.9
  },
  {
    "source": "定积分概念",
    "target": "变限积分",
    "weight": 0.85
  },
  {
    "source": "连续性",
    "target": "变限积分求导",
    "weight": 0.8
  },
  {
    "source": "极限概念",
    "target": "连续性",
    "weight": 0.95
  },
  {
    "source": "极限存在",
    "target": "函数值",
    "weight": 0.9
  },
  {
    "source": "极限存在",
    "target": "导数定义",
    "weight": 0.95
  },
  {
    "source": "导数定义",
    "target": "二阶导数",
    "weight": 0.9
  },
  {
    "source": "二阶导数",
    "target": "函数凹凸性",
    "weight": 0.9
  },
  {
    "source": "函数凹凸性",
    "target": "数列收敛",
    "weight": 0.75
  },
  {
    "source": "函数凹凸性",
    "target": "数列发散",
    "weight": 0.75
  },
  {
    "source": "等价无穷小概念",
    "target": "常用等价无穷小公式",
    "weight": 0.9
  },
  {
    "source": "常用等价无穷小公式",
    "target": "复合函数等价无穷小替换",
    "weight": 0.9
  },
  {
    "source": "复合函数等价无穷小替换",
    "target": "极限计算",
    "weight": 0.85
  },
  {
    "source": "对数恒等变形",
    "target": "极限计算",
    "weight": 0.8
  },
  {
    "source": "部分分式分解",
    "target": "极限计算",
    "weight": 0.8
  },
  {
    "source": "函数的连续性",
    "target": "连续函数代入求极限",
    "weight": 0.9
  },
  {
    "source": "连续函数代入求极限",
    "target": "极限的四则运算",
    "weight": 0.85
  },
  {
    "source": "极限的四则运算",
    "target": "分式拆项求极限",
    "weight": 0.8
  },
  {
    "source": "极限的四则运算",
    "target": "无穷大极限判定",
    "weight": 0.75
  },
  {
    "source": "极限存在与无穷小的关系",
    "target": "函数的连续性",
    "weight": 0.85
  },
  {
    "source": "多项式恒等定理",
    "target": "待定系数法",
    "weight": 0.8
  },
  {
    "source": "极限概念",
    "target": "极限的运算法则",
    "weight": 0.9
  },
  {
    "source": "极限的运算法则",
    "target": "函数连续性",
    "weight": 0.85
  },
  {
    "source": "函数连续性",
    "target": "导数定义",
    "weight": 0.9
  },
  {
    "source": "极限概念",
    "target": "导数定义",
    "weight": 0.95
  },
  {
    "source": "左右极限",
    "target": "极限存在",
    "weight": 0.9
  },
  {
    "source": "拉格朗日中值定理",
    "target": "函数差值与导数关系",
    "weight": 0.9
  },
  {
    "source": "曲线积分的参数方程计算法",
    "target": "第一类曲线积分",
    "weight": 0.9
  },
  {
    "source": "曲线积分的参数方程计算法",
    "target": "第二类曲线积分",
    "weight": 0.9
  },
  {
    "source": "第一类曲线积分",
    "target": "第二类曲线积分",
    "weight": 0.8
  },
  {
    "source": "线性组合",
    "target": "向量组的线性相关",
    "weight": 0.95
  },
  {
    "source": "线性相关的定义",
    "target": "向量组的线性相关性判断",
    "weight": 0.9
  },
  {
    "source": "矩阵乘法",
    "target": "向量组的线性表示",
    "weight": 0.85
  },
  {
    "source": "行列式的计算",
    "target": "可逆矩阵的判定",
    "weight": 0.9
  },
  {
    "source": "可逆矩阵的判定",
    "target": "可逆矩阵与初等矩阵的关系",
    "weight": 0.85
  },
  {
    "source": "可逆矩阵与初等矩阵的关系",
    "target": "初等变换不改变矩阵的秩",
    "weight": 0.9
  },
  {
    "source": "初等变换不改变矩阵的秩",
    "target": "向量组的线性相关性判断",
    "weight": 0.9
  },
  {
    "source": "向量组的秩",
    "target": "线性无关",
    "weight": 0.9
  },
  {
    "source": "矩阵的秩",
    "target": "向量组的秩",
    "weight": 0.85
  },
  {
    "source": "向量组的线性组合",
    "target": "矩阵的秩",
    "weight": 0.8
  },
  {
    "source": "换元积分法",
    "target": "定积分计算",
    "weight": 0.9
  },
  {
    "source": "偏导数概念",
    "target": "多元复合函数求偏导",
    "weight": 0.9
  },
  {
    "source": "一元复合函数求导法则",
    "target": "多元复合函数求偏导",
    "weight": 0.85
  },
  {
    "source": "特征方程求根",
    "target": "齐次方程通解",
    "weight": 0.9
  },
  {
    "source": "齐次方程通解",
    "target": "非齐次方程通解",
    "weight": 0.95
  },
  {
    "source": "指数运算法则",
    "target": "指数与根式的转化",
    "weight": 0.8
  },
  {
    "source": "特征方程",
    "target": "非齐次微分方程特解",
    "weight": 0.9
  },
  {
    "source": "非齐次微分方程特解",
    "target": "微分方程通解",
    "weight": 0.9
  },
  {
    "source": "积分区域对称性",
    "target": "第一类曲面积分",
    "weight": 0.85
  },
  {
    "source": "奇偶函数",
    "target": "第一类曲面积分",
    "weight": 0.85
  },
  {
    "source": "函数最大值",
    "target": "构造辅助函数",
    "weight": 0.8
  },
  {
    "source": "构造辅助函数",
    "target": "零点定理",
    "weight": 0.9
  },
  {
    "source": "连续函数介值定理",
    "target": "罗尔定理",
    "weight": 0.85
  },
  {
    "source": "罗尔定理",
    "target": "罗尔定理的多次应用",
    "weight": 0.9
  },
  {
    "source": "幂级数",
    "target": "幂级数的逐项求导",
    "weight": 0.9
  },
  {
    "source": "幂级数的逐项求导",
    "target": "幂级数的加减运算",
    "weight": 0.85
  },
  {
    "source": "幂级数的加减运算",
    "target": "比较系数法",
    "weight": 0.9
  },
  {
    "source": "幂级数",
    "target": "泰勒级数的唯一性",
    "weight": 0.9
  },
  {
    "source": "高阶导数",
    "target": "泰勒级数的唯一性",
    "weight": 0.85
  },
  {
    "source": "泰勒级数的唯一性",
    "target": "微分方程的幂级数解法",
    "weight": 0.9
  },
  {
    "source": "高阶导数",
    "target": "微分方程的幂级数解法",
    "weight": 0.85
  },
  {
    "source": "连续型随机变量",
    "target": "二维随机变量函数的分布",
    "weight": 0.9
  },
  {
    "source": "二维随机变量函数的分布",
    "target": "分布函数",
    "weight": 0.85
  },
  {
    "source": "矩估计",
    "target": "无偏估计",
    "weight": 0.8
  },
  {
    "source": "数学期望",
    "target": "矩估计",
    "weight": 0.95
  },
  {
    "source": "样本均值",
    "target": "矩估计",
    "weight": 0.9
  },
  {
    "source": "数学期望",
    "target": "无偏估计",
    "weight": 0.9
  },
  {
    "source": "方差",
    "target": "无偏估计",
    "weight": 0.85
  },
  {
    "source": "方差与期望的关系",
    "target": "无偏估计",
    "weight": 0.85
  },
  {
    "source": "方差的计算公式",
    "target": "无偏估计",
    "weight": 0.85
  },
  {
    "source": "数学期望的计算",
    "target": "无偏估计",
    "weight": 0.9
  },
  {
    "source": "样本均值的期望与方差",
    "target": "无偏估计",
    "weight": 0.88
  },
  {
    "source": "变限积分求导",
    "target": "导数的零点",
    "weight": 0.9
  },
  {
    "source": "偏导数计算",
    "target": "梯度计算",
    "weight": 0.95
  },
  {
    "source": "微分方程特征根",
    "target": "微分方程通解结构",
    "weight": 0.9
  },
  {
    "source": "单调有界准则",
    "target": "数列收敛",
    "weight": 0.95
  },
  {
    "source": "矩阵特征值",
    "target": "幂零矩阵性质",
    "weight": 0.85
  },
  {
    "source": "实对称矩阵",
    "target": "特征值",
    "weight": 0.9
  },
  {
    "source": "二次型",
    "target": "正交变换",
    "weight": 0.9
  },
  {
    "source": "正交变换",
    "target": "标准形",
    "weight": 0.9
  },
  {
    "source": "标准形",
    "target": "特征值",
    "weight": 0.85
  },
  {
    "source": "极限",
    "target": "等价无穷小",
    "weight": 0.9
  },
  {
    "source": "极限",
    "target": "泰勒公式",
    "weight": 0.85
  },
  {
    "source": "连续函数",
    "target": "变限积分求导",
    "weight": 0.9
  },
  {
    "source": "导数定义",
    "target": "变限积分求导",
    "weight": 0.85
  },
  {
    "source": "曲线积分",
    "target": "格林公式",
    "weight": 0.9
  },
  {
    "source": "条件极值",
    "target": "拉格朗日乘数法",
    "weight": 0.95
  },
  {
    "source": "周期函数定义",
    "target": "周期函数性质判定",
    "weight": 0.9
  },
  {
    "source": "定积分性质",
    "target": "周期函数性质判定",
    "weight": 0.85
  },
  {
    "source": "傅里叶余弦级数展开",
    "target": "常数项级数求和",
    "weight": 0.95
  },
  {
    "source": "向量线性相关性",
    "target": "矩阵的秩",
    "weight": 0.9
  },
  {
    "source": "矩阵的秩",
    "target": "矩阵秩的不等式",
    "weight": 0.85
  },
  {
    "source": "线性方程组解的判定",
    "target": "线性方程组求解",
    "weight": 0.95
  },
  {
    "source": "连续型随机变量",
    "target": "全概率公式",
    "weight": 0.8
  },
  {
    "source": "随机变量的独立性",
    "target": "条件概率",
    "weight": 0.9
  },
  {
    "source": "全概率公式",
    "target": "随机变量函数的分布",
    "weight": 0.9
  },
  {
    "source": "条件概率",
    "target": "随机变量函数的分布",
    "weight": 0.7
  },
  {
    "source": "正态分布",
    "target": "简单随机样本",
    "weight": 0.85
  },
  {
    "source": "简单随机样本",
    "target": "样本均值",
    "weight": 0.9
  },
  {
    "source": "简单随机样本",
    "target": "样本方差",
    "weight": 0.9
  },
  {
    "source": "样本均值",
    "target": "无偏估计",
    "weight": 0.8
  },
  {
    "source": "样本方差",
    "target": "无偏估计",
    "weight": 0.85
  },
  {
    "source": "样本均值",
    "target": "统计量的数字特征",
    "weight": 0.85
  },
  {
    "source": "样本方差",
    "target": "统计量的数字特征",
    "weight": 0.85
  },
  {
    "source": "无偏估计",
    "target": "统计量的数字特征",
    "weight": 0.7
  },
  {
    "source": "导数",
    "target": "函数的单调性",
    "weight": 0.95
  },
  {
    "source": "导数",
    "target": "函数的零点",
    "weight": 0.8
  },
  {
    "source": "函数的单调性",
    "target": "函数的零点",
    "weight": 0.85
  },
  {
    "source": "特征根",
    "target": "特征方程",
    "weight": 0.9
  },
  {
    "source": "特征方程",
    "target": "常系数齐次线性微分方程",
    "weight": 0.95
  },
  {
    "source": "单调有界准则",
    "target": "数列极限",
    "weight": 0.9
  },
  {
    "source": "矩阵乘法",
    "target": "逆矩阵判定",
    "weight": 0.85
  },
  {
    "source": "特征值",
    "target": "二次型的标准型",
    "weight": 0.9
  },
  {
    "source": "二次型的标准型",
    "target": "二次曲面",
    "weight": 0.85
  },
  {
    "source": "随机变量的独立性",
    "target": "最大值函数的分布",
    "weight": 0.9
  },
  {
    "source": "分布函数的定义",
    "target": "最大值函数的分布",
    "weight": 0.9
  },
  {
    "source": "相关系数",
    "target": "线性相关",
    "weight": 0.85
  },
  {
    "source": "数学期望的性质",
    "target": "期望的计算",
    "weight": 0.8
  },
  {
    "source": "可分离变量的微分方程",
    "target": "求不定积分",
    "weight": 0.85
  },
  {
    "source": "初值条件",
    "target": "确定积分常数",
    "weight": 0.9
  },
  {
    "source": "偏导数",
    "target": "隐函数求导",
    "weight": 0.9
  },
  {
    "source": "隐函数求导",
    "target": "切线方程",
    "weight": 0.85
  },
  {
    "source": "幂级数",
    "target": "收敛中心",
    "weight": 0.9
  },
  {
    "source": "收敛区间",
    "target": "收敛域",
    "weight": 0.95
  },
  {
    "source": "变量代换",
    "target": "幂级数收敛域计算",
    "weight": 0.85
  },
  {
    "source": "高斯公式",
    "target": "补面法",
    "weight": 0.95
  },
  {
    "source": "二重积分",
    "target": "极坐标变换",
    "weight": 0.85
  },
  {
    "source": "极坐标",
    "target": "二重积分计算",
    "weight": 0.85
  },
  {
    "source": "线性无关",
    "target": "可逆矩阵",
    "weight": 0.9
  },
  {
    "source": "矩阵乘法",
    "target": "相似矩阵",
    "weight": 0.8
  },
  {
    "source": "相似矩阵",
    "target": "特征值",
    "weight": 0.95
  },
  {
    "source": "泊松分布的数字特征",
    "target": "方差与期望的关系",
    "weight": 0.85
  },
  {
    "source": "方差与期望的关系",
    "target": "泊松分布的概率计算",
    "weight": 0.8
  },
  {
    "source": "卡方分布的方差性质",
    "target": "样本方差的方差计算",
    "weight": 0.9
  },
  {
    "source": "正态总体抽样分布定理",
    "target": "样本方差的方差计算",
    "weight": 0.9
  },
  {
    "source": "方差公式",
    "target": "样本方差的二阶矩计算",
    "weight": 0.85
  },
  {
    "source": "样本均值与样本方差的独立性",
    "target": "独立随机变量和的方差计算",
    "weight": 0.95
  },
  {
    "source": "独立随机变量和的方差计算",
    "target": "统计量T的方差",
    "weight": 0.9
  },
  {
    "source": "泰勒公式",
    "target": "等价无穷小",
    "weight": 0.85
  },
  {
    "source": "定积分概念",
    "target": "变上限积分",
    "weight": 0.9
  },
  {
    "source": "导数概念",
    "target": "变上限积分求导",
    "weight": 0.95
  },
  {
    "source": "二重积分概念",
    "target": "二重积分计算",
    "weight": 0.9
  },
  {
    "source": "奇偶函数性质",
    "target": "对称区间积分性质",
    "weight": 0.85
  },
  {
    "source": "古典概型",
    "target": "条件概率",
    "weight": 0.85
  },
  {
    "source": "古典概型",
    "target": "二维离散型随机变量的概率分布",
    "weight": 0.9
  },
  {
    "source": "连续型随机变量的概率密度",
    "target": "矩估计",
    "weight": 0.9
  },
  {
    "source": "连续型随机变量的概率密度",
    "target": "最大似然估计",
    "weight": 0.9
  },
  {
    "source": "洛必达法则",
    "target": "未定式极限",
    "weight": 0.9
  },
  {
    "source": "等价无穷小",
    "target": "未定式极限",
    "weight": 0.85
  },
  {
    "source": "二重积分概念",
    "target": "二重积分的对称性与奇偶性",
    "weight": 0.9
  },
  {
    "source": "定积分概念",
    "target": "变上限积分函数",
    "weight": 0.9
  },
  {
    "source": "导数判断单调性",
    "target": "变上限积分函数性质",
    "weight": 0.8
  },
  {
    "source": "数列极限",
    "target": "级数收敛",
    "weight": 0.9
  },
  {
    "source": "绝对收敛",
    "target": "级数收敛",
    "weight": 1.0
  },
  {
    "source": "p级数敛散性",
    "target": "级数收敛",
    "weight": 0.8
  },
  {
    "source": "p级数敛散性",
    "target": "级数发散",
    "weight": 0.8
  },
  {
    "source": "数列极限的定义",
    "target": "级数收敛的必要条件",
    "weight": 0.8
  },
  {
    "source": "级数收敛的必要条件",
    "target": "正项级数的比较判别法",
    "weight": 0.85
  },
  {
    "source": "数列极限的定义",
    "target": "正项级数的比较判别法",
    "weight": 0.75
  },
  {
    "source": "基变换",
    "target": "过渡矩阵的定义",
    "weight": 0.9
  },
  {
    "source": "行列式",
    "target": "分块矩阵的行列式",
    "weight": 0.9
  },
  {
    "source": "分块矩阵",
    "target": "分块矩阵的行列式",
    "weight": 0.9
  },
  {
    "source": "随机变量的独立性",
    "target": "随机变量函数的分布",
    "weight": 0.85
  },
  {
    "source": "随机变量函数的分布",
    "target": "分布函数",
    "weight": 0.8
  },
  {
    "source": "分布函数",
    "target": "间断点判断",
    "weight": 0.75
  },
  {
    "source": "多元复合函数求导法则",
    "target": "一阶偏导数",
    "weight": 0.9
  },
  {
    "source": "二阶常系数线性齐次微分方程",
    "target": "二阶常系数线性非齐次微分方程",
    "weight": 0.9
  },
  {
    "source": "二阶常系数线性齐次微分方程",
    "target": "待定系数法求特解",
    "weight": 0.8
  },
  {
    "source": "待定系数法求特解",
    "target": "非齐次方程通解",
    "weight": 0.9
  },
  {
    "source": "非齐次方程通解",
    "target": "初值条件定常数",
    "weight": 0.85
  },
  {
    "source": "驻点",
    "target": "二元函数极值判别法",
    "weight": 0.85
  },
  {
    "source": "二阶偏导数",
    "target": "二元函数极值判别法",
    "weight": 0.9
  },
  {
    "source": "二元函数极值判别法",
    "target": "极值",
    "weight": 0.95
  },
  {
    "source": "曲线交点",
    "target": "定积分求面积",
    "weight": 0.9
  },
  {
    "source": "定积分计算",
    "target": "数列通项公式",
    "weight": 0.9
  },
  {
    "source": "数列通项公式",
    "target": "裂项相消法",
    "weight": 0.85
  },
  {
    "source": "裂项相消法",
    "target": "常数项级数求和",
    "weight": 0.8
  },
  {
    "source": "数列极限",
    "target": "常数项级数求和",
    "weight": 0.9
  },
  {
    "source": "常数项级数",
    "target": "交错级数",
    "weight": 0.7
  },
  {
    "source": "交错级数",
    "target": "幂级数",
    "weight": 0.8
  },
  {
    "source": "幂级数收敛域",
    "target": "幂级数和函数",
    "weight": 0.85
  },
  {
    "source": "幂级数和函数",
    "target": "常数项级数求和",
    "weight": 0.9
  },
  {
    "source": "极限",
    "target": "幂指函数极限",
    "weight": 0.9
  },
  {
    "source": "幂指函数极限",
    "target": "第二重要极限",
    "weight": 0.85
  },
  {
    "source": "多元复合函数求导法则",
    "target": "隐函数求偏导",
    "weight": 0.9
  },
  {
    "source": "隐函数存在定理",
    "target": "隐函数求偏导",
    "weight": 0.85
  },
  {
    "source": "反常积分",
    "target": "反常积分敛散性判断",
    "weight": 0.9
  },
  {
    "source": "瑕积分",
    "target": "反常积分敛散性判断",
    "weight": 0.85
  },
  {
    "source": "无穷限反常积分",
    "target": "反常积分敛散性判断",
    "weight": 0.85
  },
  {
    "source": "n项和的极限",
    "target": "定积分的定义",
    "weight": 0.9
  },
  {
    "source": "n项和的极限",
    "target": "二重积分的定义",
    "weight": 0.9
  },
  {
    "source": "定积分的定义",
    "target": "二重积分的定义",
    "weight": 0.8
  },
  {
    "source": "定积分",
    "target": "二重积分",
    "weight": 0.9
  },
  {
    "source": "二重积分",
    "target": "累次积分",
    "weight": 0.9
  },
  {
    "source": "矩阵的特征值",
    "target": "相似对角化",
    "weight": 0.9
  },
  {
    "source": "矩阵的秩",
    "target": "矩阵的特征值",
    "weight": 0.8
  },
  {
    "source": "离散概率分布",
    "target": "无偏估计量",
    "weight": 0.9
  },
  {
    "source": "简单随机样本",
    "target": "无偏估计量",
    "weight": 0.85
  },
  {
    "source": "无偏估计量",
    "target": "估计量的方差",
    "weight": 0.9
  },
  {
    "source": "未定式求极限",
    "target": "1^∞型极限",
    "weight": 0.95
  },
  {
    "source": "1^∞型极限",
    "target": "e的抬起法",
    "weight": 0.9
  },
  {
    "source": "幂指函数求极限",
    "target": "指数对数变换",
    "weight": 0.95
  },
  {
    "source": "指数对数变换",
    "target": "等价无穷小代换",
    "weight": 0.85
  },
  {
    "source": "等价无穷小代换",
    "target": "有理函数极限",
    "weight": 0.9
  },
  {
    "source": "对数运算性质",
    "target": "等价无穷小代换",
    "weight": 0.75
  },
  {
    "source": "偏导数的概念与计算",
    "target": "隐函数求导法则",
    "weight": 0.9
  },
  {
    "source": "复合函数求导法则",
    "target": "隐函数求导法则",
    "weight": 0.95
  },
  {
    "source": "瑕点判断",
    "target": "反常积分(瑕积分)",
    "weight": 0.85
  },
  {
    "source": "瑕点判断",
    "target": "积分区间的拆分",
    "weight": 0.8
  },
  {
    "source": "定积分的区间可加性",
    "target": "反常积分的计算",
    "weight": 0.8
  },
  {
    "source": "反常积分",
    "target": "比较判别法的极限形式",
    "weight": 0.9
  },
  {
    "source": "极限",
    "target": "比较判别法的极限形式",
    "weight": 0.85
  },
  {
    "source": "矩阵的秩",
    "target": "矩阵乘法的秩",
    "weight": 0.9
  },
  {
    "source": "矩阵的特征值",
    "target": "矩阵多项式的特征值",
    "weight": 0.9
  },
  {
    "source": "实对称矩阵",
    "target": "矩阵可相似对角化",
    "weight": 0.9
  },
  {
    "source": "矩阵的特征值",
    "target": "矩阵可相似对角化",
    "weight": 0.8
  },
  {
    "source": "矩阵相似",
    "target": "矩阵的秩",
    "weight": 0.9
  },
  {
    "source": "分布函数的定义",
    "target": "利用分布函数求单点概率",
    "weight": 0.95
  },
  {
    "source": "离散型随机变量",
    "target": "离散型随机变量的分布函数",
    "weight": 0.85
  },
  {
    "source": "连续型随机变量",
    "target": "连续型随机变量的分布函数",
    "weight": 0.85
  },
  {
    "source": "连续型随机变量",
    "target": "概率密度的性质",
    "weight": 0.9
  },
  {
    "source": "概率密度",
    "target": "正态分布",
    "weight": 0.8
  },
  {
    "source": "概率密度",
    "target": "均匀分布",
    "weight": 0.8
  },
  {
    "source": "反常积分",
    "target": "概率密度性质",
    "weight": 0.85
  },
  {
    "source": "复合函数求导",
    "target": "参数方程求导",
    "weight": 0.85
  },
  {
    "source": "参数方程求导",
    "target": "参数方程二阶导数",
    "weight": 0.9
  },
  {
    "source": "二阶导数",
    "target": "拐点",
    "weight": 0.9
  },
  {
    "source": "数列极限",
    "target": "交错级数审敛法",
    "weight": 0.85
  },
  {
    "source": "交错级数审敛法",
    "target": "幂级数收敛域",
    "weight": 0.8
  },
  {
    "source": "二阶偏导数",
    "target": "多元函数极值",
    "weight": 0.9
  },
  {
    "source": "对数函数性质",
    "target": "定积分比较",
    "weight": 0.8
  },
  {
    "source": "三角函数性质",
    "target": "定积分比较",
    "weight": 0.8
  },
  {
    "source": "初等变换",
    "target": "初等矩阵",
    "weight": 0.9
  },
  {
    "source": "初等矩阵",
    "target": "逆矩阵",
    "weight": 0.85
  },
  {
    "source": "伴随矩阵",
    "target": "矩阵的秩",
    "weight": 0.85
  },
  {
    "source": "矩阵的秩",
    "target": "齐次线性方程组",
    "weight": 0.85
  },
  {
    "source": "齐次线性方程组",
    "target": "基础解系",
    "weight": 0.9
  },
  {
    "source": "二维随机变量的概率分布",
    "target": "随机变量函数的概率分布",
    "weight": 0.9
  },
  {
    "source": "二维随机变量的概率分布",
    "target": "相关系数",
    "weight": 0.85
  },
  {
    "source": "随机变量的期望与方差",
    "target": "相关系数",
    "weight": 0.9
  },
  {
    "source": "正态总体",
    "target": "最大似然估计",
    "weight": 0.8
  },
  {
    "source": "最大似然估计",
    "target": "估计量的期望与方差",
    "weight": 0.9
  },
  {
    "source": "样本均值与样本方差",
    "target": "最大似然估计",
    "weight": 0.7
  },
  {
    "source": "二阶导数",
    "target": "拐点判定",
    "weight": 0.9
  },
  {
    "source": "莱布尼茨判别法",
    "target": "级数敛散性判定",
    "weight": 0.9
  },
  {
    "source": "复合函数求导法则",
    "target": "偏导数",
    "weight": 0.85
  },
  {
    "source": "二阶偏导数",
    "target": "多元函数极值的充分条件",
    "weight": 0.9
  },
  {
    "source": "随机变量的独立性",
    "target": "随机变量的期望",
    "weight": 0.85
  },
  {
    "source": "导数",
    "target": "弧微分",
    "weight": 0.8
  },
  {
    "source": "弧微分",
    "target": "定积分求弧长",
    "weight": 0.9
  },
  {
    "source": "不定积分基本公式",
    "target": "牛顿-莱布尼茨公式",
    "weight": 0.9
  },
  {
    "source": "一阶线性微分方程",
    "target": "常数变易法",
    "weight": 0.95
  },
  {
    "source": "微分方程通解",
    "target": "初值问题求解",
    "weight": 0.9
  },
  {
    "source": "复合函数求导法则",
    "target": "二阶偏导数",
    "weight": 0.85
  },
  {
    "source": "斯托克斯公式",
    "target": "空间曲线积分计算",
    "weight": 0.9
  },
  {
    "source": "第二型曲面积分",
    "target": "转换投影法",
    "weight": 0.9
  },
  {
    "source": "偏导数计算",
    "target": "转换投影法",
    "weight": 0.8
  },
  {
    "source": "转换投影法",
    "target": "二重积分计算",
    "weight": 0.9
  },
  {
    "source": "复合函数求导法则",
    "target": "抽象函数偏导数",
    "weight": 0.95
  },
  {
    "source": "极值必要条件",
    "target": "偏导数求值",
    "weight": 0.85
  },
  {
    "source": "导数的运算",
    "target": "函数单调性",
    "weight": 0.9
  },
  {
    "source": "极限的计算",
    "target": "零点定理",
    "weight": 0.85
  },
  {
    "source": "函数单调性",
    "target": "零点定理",
    "weight": 0.8
  },
  {
    "source": "零点定理",
    "target": "方程根的个数讨论",
    "weight": 0.95
  },
  {
    "source": "函数零点",
    "target": "方程的根",
    "weight": 0.9
  },
  {
    "source": "卡方分布",
    "target": "统计量的期望",
    "weight": 0.9
  },
  {
    "source": "卡方分布",
    "target": "统计量的方差",
    "weight": 0.9
  },
  {
    "source": "函数极限",
    "target": "曲线渐近线",
    "weight": 0.9
  },
  {
    "source": "导数定义",
    "target": "导数四则运算",
    "weight": 0.85
  },
  {
    "source": "多元函数极限",
    "target": "多元函数连续性",
    "weight": 0.9
  },
  {
    "source": "多元函数连续性",
    "target": "多元函数可微性",
    "weight": 0.95
  },
  {
    "source": "多元函数极限",
    "target": "多元函数可微性",
    "weight": 0.85
  },
  {
    "source": "极限计算",
    "target": "垂直渐近线",
    "weight": 0.9
  },
  {
    "source": "极限计算",
    "target": "水平渐近线",
    "weight": 0.9
  },
  {
    "source": "极限计算",
    "target": "斜渐近线",
    "weight": 0.85
  },
  {
    "source": "导数概念",
    "target": "导数的乘法法则",
    "weight": 0.85
  },
  {
    "source": "二元函数极限",
    "target": "二元函数连续性",
    "weight": 0.9
  },
  {
    "source": "二元函数极限",
    "target": "二元函数可微性",
    "weight": 0.85
  },
  {
    "source": "高阶无穷小",
    "target": "二元函数可微性",
    "weight": 0.8
  },
  {
    "source": "变上限积分求导",
    "target": "函数单调性",
    "weight": 0.9
  },
  {
    "source": "变量代换",
    "target": "定积分计算",
    "weight": 0.85
  },
  {
    "source": "奇偶函数在对称区间的积分性质",
    "target": "定积分计算",
    "weight": 0.9
  },
  {
    "source": "第一类曲面积分",
    "target": "二重积分计算",
    "weight": 0.9
  },
  {
    "source": "矩阵特征值",
    "target": "矩阵多项式的特征值",
    "weight": 0.9
  },
  {
    "source": "相似对角化",
    "target": "矩阵的秩",
    "weight": 0.85
  },
  {
    "source": "矩阵特征值",
    "target": "矩阵的秩",
    "weight": 0.8
  },
  {
    "source": "条件概率定义",
    "target": "条件概率计算",
    "weight": 0.9
  },
  {
    "source": "互斥事件",
    "target": "条件概率计算",
    "weight": 0.8
  },
  {
    "source": "对立事件概率",
    "target": "条件概率计算",
    "weight": 0.7
  },
  {
    "source": "特征值",
    "target": "线性方程组求解",
    "weight": 0.8
  },
  {
    "source": "矩阵的秩",
    "target": "行列式的计算",
    "weight": 0.8
  },
  {
    "source": "二次型",
    "target": "实对称矩阵",
    "weight": 0.9
  },
  {
    "source": "行列式的计算",
    "target": "特征值的计算",
    "weight": 0.85
  },
  {
    "source": "特征值的计算",
    "target": "特征向量的计算",
    "weight": 0.9
  },
  {
    "source": "齐次线性方程组",
    "target": "特征向量的计算",
    "weight": 0.85
  },
  {
    "source": "齐次线性方程组求解",
    "target": "特征向量",
    "weight": 0.9
  },
  {
    "source": "特征向量",
    "target": "向量的单位化",
    "weight": 0.85
  },
  {
    "source": "向量的单位化",
    "target": "正交矩阵",
    "weight": 0.85
  },
  {
    "source": "边缘分布",
    "target": "联合分布律",
    "weight": 0.8
  },
  {
    "source": "联合分布律",
    "target": "二维离散型随机变量概率计算",
    "weight": 0.9
  },
  {
    "source": "数学期望",
    "target": "方差计算公式",
    "weight": 0.9
  },
  {
    "source": "数学期望",
    "target": "协方差计算公式",
    "weight": 0.9
  },
  {
    "source": "方差",
    "target": "协方差性质",
    "weight": 0.85
  },
  {
    "source": "正态分布",
    "target": "概率密度函数",
    "weight": 0.85
  },
  {
    "source": "对数似然函数",
    "target": "似然方程",
    "weight": 0.9
  },
  {
    "source": "似然方程",
    "target": "最大似然估计值",
    "weight": 0.95
  },
  {
    "source": "最大似然估计值",
    "target": "最大似然估计量",
    "weight": 0.85
  },
  {
    "source": "期望的线性性质",
    "target": "无偏估计量",
    "weight": 0.8
  },
  {
    "source": "方差与期望的关系公式",
    "target": "无偏估计量",
    "weight": 0.85
  },
  {
    "source": "极限概念",
    "target": "泰勒展开",
    "weight": 0.9
  },
  {
    "source": "反三角函数求导",
    "target": "泰勒展开",
    "weight": 0.8
  },
  {
    "source": "导数概念",
    "target": "偏导数",
    "weight": 0.85
  },
  {
    "source": "偏导数",
    "target": "空间曲面的切平面方程",
    "weight": 0.95
  },
  {
    "source": "定积分",
    "target": "傅里叶级数系数计算",
    "weight": 0.9
  },
  {
    "source": "傅里叶级数",
    "target": "狄利克雷收敛定理",
    "weight": 0.95
  },
  {
    "source": "圆与椭圆方程",
    "target": "二重积分",
    "weight": 0.7
  },
  {
    "source": "矩阵乘法",
    "target": "可逆矩阵",
    "weight": 0.7
  },
  {
    "source": "可逆矩阵",
    "target": "向量组等价",
    "weight": 0.85
  },
  {
    "source": "特征值与特征向量",
    "target": "矩阵相似",
    "weight": 0.95
  },
  {
    "source": "实对称矩阵",
    "target": "矩阵相似对角化",
    "weight": 0.9
  },
  {
    "source": "矩阵相似对角化",
    "target": "矩阵相似",
    "weight": 0.9
  },
  {
    "source": "标准正态分布",
    "target": "正态分布标准化",
    "weight": 0.9
  },
  {
    "source": "一般正态分布",
    "target": "正态分布标准化",
    "weight": 0.95
  },
  {
    "source": "正态分布标准化",
    "target": "正态分布概率计算",
    "weight": 0.85
  },
  {
    "source": "t分布",
    "target": "t分布与F分布的关系",
    "weight": 0.9
  },
  {
    "source": "F分布",
    "target": "t分布与F分布的关系",
    "weight": 0.9
  },
  {
    "source": "t分布与F分布的关系",
    "target": "上侧分位数概率计算",
    "weight": 0.85
  },
  {
    "source": "极限概念",
    "target": "泰勒公式求极限",
    "weight": 0.9
  },
  {
    "source": "泰勒公式",
    "target": "常见函数的泰勒展开",
    "weight": 0.85
  },
  {
    "source": "常见函数的泰勒展开",
    "target": "泰勒公式求极限",
    "weight": 0.9
  },
  {
    "source": "偏导数概念",
    "target": "隐函数求偏导",
    "weight": 0.85
  },
  {
    "source": "偏导数概念",
    "target": "曲面的切平面方程",
    "weight": 0.9
  },
  {
    "source": "隐函数求偏导",
    "target": "曲面的切平面方程",
    "weight": 0.85
  },
  {
    "source": "对数似然函数",
    "target": "求导运算",
    "weight": 0.9
  },
  {
    "source": "求导运算",
    "target": "极值条件",
    "weight": 0.9
  },
  {
    "source": "极值条件",
    "target": "极大似然估计量",
    "weight": 0.95
  },
  {
    "source": "极限",
    "target": "渐近线",
    "weight": 0.9
  },
  {
    "source": "一阶导数",
    "target": "函数单调性",
    "weight": 0.95
  },
  {
    "source": "二阶导数",
    "target": "曲线的凹凸性",
    "weight": 0.95
  },
  {
    "source": "曲线的凹凸性",
    "target": "函数不等式",
    "weight": 0.9
  },
  {
    "source": "累次积分",
    "target": "交换积分次序",
    "weight": 0.95
  },
  {
    "source": "二重积分的概念",
    "target": "极坐标下的二重积分计算",
    "weight": 0.9
  },
  {
    "source": "定积分的概念",
    "target": "定积分的最值问题",
    "weight": 0.8
  },
  {
    "source": "多元函数极值",
    "target": "定积分的最值问题",
    "weight": 0.85
  },
  {
    "source": "变限积分求导",
    "target": "洛必达法则",
    "weight": 0.9
  },
  {
    "source": "导数概念",
    "target": "隐函数求导",
    "weight": 0.9
  },
  {
    "source": "隐函数一阶求导",
    "target": "隐函数二阶求导",
    "weight": 0.95
  },
  {
    "source": "二阶导数",
    "target": "函数极值判定",
    "weight": 0.9
  },
  {
    "source": "偏导数概念",
    "target": "多元复合函数求导法则",
    "weight": 0.9
  },
  {
    "source": "一元复合函数求导",
    "target": "多元复合函数求导法则",
    "weight": 0.85
  },
  {
    "source": "多元复合函数求导法则",
    "target": "偏导数的计算",
    "weight": 0.85
  },
  {
    "source": "偏导数的计算",
    "target": "变量代换",
    "weight": 0.8
  },
  {
    "source": "变量代换",
    "target": "二阶常系数非齐次线性微分方程",
    "weight": 0.85
  },
  {
    "source": "二阶常系数非齐次线性微分方程",
    "target": "微分方程初值问题",
    "weight": 0.9
  },
  {
    "source": "数学期望",
    "target": "二阶原点矩",
    "weight": 0.85
  },
  {
    "source": "二阶原点矩",
    "target": "矩估计法",
    "weight": 0.9
  },
  {
    "source": "大数定律",
    "target": "估计量相合性",
    "weight": 0.85
  },
  {
    "source": "连续性",
    "target": "二阶导数",
    "weight": 0.7
  },
  {
    "source": "二阶导数异号",
    "target": "拐点",
    "weight": 0.95
  },
  {
    "source": "齐次微分方程的解",
    "target": "非齐次微分方程的解的结构",
    "weight": 0.8
  },
  {
    "source": "二次型的矩阵表示",
    "target": "矩阵的合同",
    "weight": 0.85
  },
  {
    "source": "矩阵的合同",
    "target": "二次型的标准形",
    "weight": 0.9
  },
  {
    "source": "二次型",
    "target": "二次型的标准形",
    "weight": 0.95
  },
  {
    "source": "随机事件",
    "target": "事件概率",
    "weight": 0.9
  },
  {
    "source": "事件概率",
    "target": "概率不等式",
    "weight": 0.8
  },
  {
    "source": "事件包含关系",
    "target": "概率的单调性",
    "weight": 0.9
  },
  {
    "source": "方差公式",
    "target": "二阶矩的计算",
    "weight": 0.9
  },
  {
    "source": "不相关性质",
    "target": "期望乘积分解",
    "weight": 0.9
  },
  {
    "source": "0/0型未定式",
    "target": "洛必达法则",
    "weight": 0.95
  },
  {
    "source": "0/0型未定式",
    "target": "等价无穷小替换",
    "weight": 0.9
  },
  {
    "source": "奇偶函数在对称区间上的积分性质",
    "target": "定积分计算",
    "weight": 0.9
  },
  {
    "source": "隐函数求导",
    "target": "全微分计算",
    "weight": 0.9
  },
  {
    "source": "偏导数概念",
    "target": "隐函数求导公式",
    "weight": 0.9
  },
  {
    "source": "隐函数求导公式",
    "target": "全微分计算",
    "weight": 0.85
  },
  {
    "source": "偏导数概念",
    "target": "全微分计算",
    "weight": 0.9
  },
  {
    "source": "截面法(先二后一)",
    "target": "三重积分计算",
    "weight": 0.9
  },
  {
    "source": "积分区域的对称性",
    "target": "三重积分计算",
    "weight": 0.85
  },
  {
    "source": "三重积分计算",
    "target": "定积分计算",
    "weight": 0.9
  },
  {
    "source": "行列式按行(列)展开定理",
    "target": "递推法计算行列式",
    "weight": 0.9
  },
  {
    "source": "递推法计算行列式",
    "target": "n阶行列式计算",
    "weight": 0.85
  },
  {
    "source": "泰勒公式",
    "target": "极限计算",
    "weight": 0.9
  },
  {
    "source": "等价无穷小代换",
    "target": "极限计算",
    "weight": 0.85
  },
  {
    "source": "极限的概念与性质",
    "target": "洛必达法则",
    "weight": 0.9
  },
  {
    "source": "导数计算",
    "target": "洛必达法则",
    "weight": 0.95
  },
  {
    "source": "导数的概念",
    "target": "导数的几何意义",
    "weight": 0.9
  },
  {
    "source": "切线方程",
    "target": "建立微分方程",
    "weight": 0.85
  },
  {
    "source": "导数计算",
    "target": "建立微分方程",
    "weight": 0.8
  },
  {
    "source": "平面图形的面积",
    "target": "建立微分方程",
    "weight": 0.8
  },
  {
    "source": "可分离变量的微分方程",
    "target": "通解",
    "weight": 0.9
  },
  {
    "source": "初值条件",
    "target": "特解",
    "weight": 0.9
  },
  {
    "source": "通解",
    "target": "特解",
    "weight": 0.9
  },
  {
    "source": "向量组的线性表示",
    "target": "齐次线性方程组有非零解",
    "weight": 0.9
  },
  {
    "source": "向量组的线性相关性",
    "target": "齐次线性方程组有非零解",
    "weight": 0.9
  },
  {
    "source": "齐次线性方程组有非零解",
    "target": "行列式的计算",
    "weight": 0.85
  },
  {
    "source": "行列式的计算",
    "target": "齐次线性方程组求解",
    "weight": 0.8
  },
  {
    "source": "连续型随机变量概率计算",
    "target": "负二项分布",
    "weight": 0.8
  },
  {
    "source": "独立重复试验",
    "target": "负二项分布",
    "weight": 0.9
  },
  {
    "source": "负二项分布",
    "target": "离散型随机变量期望",
    "weight": 0.9
  },
  {
    "source": "矩阵的迹",
    "target": "矩阵相似",
    "weight": 0.9
  },
  {
    "source": "行列式",
    "target": "矩阵相似",
    "weight": 0.9
  },
  {
    "source": "等比数列求和",
    "target": "逐项求导法",
    "weight": 0.9
  },
  {
    "source": "导数运算",
    "target": "逐项求导法",
    "weight": 0.85
  },
  {
    "source": "逐项求导法",
    "target": "幂级数求和",
    "weight": 0.9
  },
  {
    "source": "幂级数性质",
    "target": "幂级数求和",
    "weight": 0.8
  },
  {
    "source": "幂级数求和",
    "target": "离散型随机变量的数学期望",
    "weight": 0.85
  },
  {
    "source": "概率分布",
    "target": "离散型随机变量的数学期望",
    "weight": 0.8
  },
  {
    "source": "概率密度函数",
    "target": "数学期望",
    "weight": 1.0
  },
  {
    "source": "定积分计算",
    "target": "数学期望",
    "weight": 0.9
  },
  {
    "source": "概率密度函数",
    "target": "似然函数",
    "weight": 1.0
  },
  {
    "source": "似然函数",
    "target": "最大似然估计法",
    "weight": 0.95
  },
  {
    "source": "对数似然函数",
    "target": "导数与单调性",
    "weight": 0.85
  },
  {
    "source": "导数与单调性",
    "target": "最大似然估计",
    "weight": 0.9
  },
  {
    "source": "反常积分的定义",
    "target": "反常积分的计算",
    "weight": 0.9
  },
  {
    "source": "反常积分的定义",
    "target": "反常积分的收敛性",
    "weight": 0.85
  },
  {
    "source": "反常积分的计算",
    "target": "反常积分的收敛性",
    "weight": 0.8
  },
  {
    "source": "原函数的定义",
    "target": "不定积分计算",
    "weight": 0.85
  },
  {
    "source": "函数的可导性",
    "target": "函数的连续性",
    "weight": 0.95
  },
  {
    "source": "齐次方程的解",
    "target": "非齐次方程解的性质",
    "weight": 0.9
  },
  {
    "source": "非齐次方程解的性质",
    "target": "微分方程求解",
    "weight": 0.8
  },
  {
    "source": "极限的定义",
    "target": "函数的连续性",
    "weight": 0.9
  },
  {
    "source": "极限的定义",
    "target": "函数的间断点",
    "weight": 0.85
  },
  {
    "source": "去心邻域",
    "target": "极限的定义",
    "weight": 0.9
  },
  {
    "source": "右极限",
    "target": "函数的连续性",
    "weight": 0.8
  },
  {
    "source": "矩阵相似的定义",
    "target": "相似矩阵的性质",
    "weight": 0.9
  },
  {
    "source": "矩阵转置的性质",
    "target": "相似矩阵的性质",
    "weight": 0.7
  },
  {
    "source": "矩阵求逆的性质",
    "target": "相似矩阵的性质",
    "weight": 0.7
  },
  {
    "source": "配方法化二次型为标准形",
    "target": "正负惯性指数",
    "weight": 0.9
  },
  {
    "source": "特征值法化二次型为标准形",
    "target": "正负惯性指数",
    "weight": 0.9
  },
  {
    "source": "正负惯性指数",
    "target": "惯性定理",
    "weight": 0.85
  },
  {
    "source": "正负惯性指数",
    "target": "二次曲面方程",
    "weight": 0.8
  },
  {
    "source": "正态分布标准化",
    "target": "标准正态分布的分布函数",
    "weight": 0.9
  },
  {
    "source": "标准正态分布的分布函数",
    "target": "分布函数的性质",
    "weight": 0.8
  },
  {
    "source": "二项分布",
    "target": "数学期望",
    "weight": 0.8
  },
  {
    "source": "分布列",
    "target": "数学期望",
    "weight": 0.9
  },
  {
    "source": "二项分布",
    "target": "方差",
    "weight": 0.8
  },
  {
    "source": "数学期望",
    "target": "协方差",
    "weight": 0.9
  },
  {
    "source": "等价无穷小替换",
    "target": "0/0型未定式",
    "weight": 0.85
  },
  {
    "source": "0/0型未定式",
    "target": "极限计算",
    "weight": 0.8
  },
  {
    "source": "多元函数",
    "target": "隐函数求导",
    "weight": 0.7
  },
  {
    "source": "隐函数求导",
    "target": "偏导数",
    "weight": 0.85
  },
  {
    "source": "偏导数",
    "target": "全微分",
    "weight": 0.95
  },
  {
    "source": "泰勒公式",
    "target": "幂级数展开",
    "weight": 0.9
  },
  {
    "source": "麦克劳林展开",
    "target": "泰勒系数与高阶导数的关系",
    "weight": 0.9
  },
  {
    "source": "特征方程与特征根",
    "target": "二阶常系数齐次微分方程通解",
    "weight": 0.95
  },
  {
    "source": "二阶常系数齐次微分方程通解",
    "target": "初值问题定解",
    "weight": 0.85
  },
  {
    "source": "偏导数",
    "target": "偏导积分求二元函数",
    "weight": 0.9
  },
  {
    "source": "不定积分",
    "target": "偏导积分求二元函数",
    "weight": 0.9
  },
  {
    "source": "偏导积分求二元函数",
    "target": "积分与路径无关",
    "weight": 0.85
  },
  {
    "source": "三重积分计算",
    "target": "先二后一法",
    "weight": 0.85
  },
  {
    "source": "拉格朗日中值定理",
    "target": "级数收敛性证明",
    "weight": 0.85
  },
  {
    "source": "比较判别法",
    "target": "级数收敛性证明",
    "weight": 0.9
  },
  {
    "source": "比较判别法",
    "target": "级数收敛",
    "weight": 0.85
  },
  {
    "source": "级数收敛",
    "target": "数列极限",
    "weight": 0.9
  },
  {
    "source": "微分中值定理",
    "target": "数列极限",
    "weight": 0.85
  },
  {
    "source": "初等行变换",
    "target": "矩阵方程求解",
    "weight": 0.95
  },
  {
    "source": "增广矩阵",
    "target": "初等行变换",
    "weight": 0.85
  },
  {
    "source": "初等行变换",
    "target": "行最简形矩阵",
    "weight": 0.9
  },
  {
    "source": "行最简形矩阵",
    "target": "线性方程组解的判定",
    "weight": 0.95
  },
  {
    "source": "线性方程组解的判定",
    "target": "无穷多解",
    "weight": 0.9
  },
  {
    "source": "线性方程组解的判定",
    "target": "无解",
    "weight": 0.9
  },
  {
    "source": "线性方程组解的判定",
    "target": "唯一解",
    "weight": 0.9
  },
  {
    "source": "无穷多解",
    "target": "自由变量",
    "weight": 0.85
  },
  {
    "source": "定积分计算",
    "target": "期望",
    "weight": 0.9
  },
  {
    "source": "概率密度函数",
    "target": "期望",
    "weight": 0.95
  },
  {
    "source": "期望",
    "target": "无偏估计",
    "weight": 0.9
  },
  {
    "source": "等价无穷小替换",
    "target": "求极限",
    "weight": 0.9
  },
  {
    "source": "求极限",
    "target": "连续性",
    "weight": 0.95
  },
  {
    "source": "函数可导",
    "target": "导数判定单调性",
    "weight": 0.85
  },
  {
    "source": "导数判定单调性",
    "target": "绝对值函数单调性",
    "weight": 0.8
  },
  {
    "source": "向量单位化",
    "target": "方向导数",
    "weight": 0.8
  },
  {
    "source": "幂级数展开",
    "target": "高阶导数",
    "weight": 0.85
  },
  {
    "source": "导数",
    "target": "偏导数",
    "weight": 0.9
  },
  {
    "source": "复数特征根",
    "target": "常系数齐次线性微分方程",
    "weight": 0.85
  },
  {
    "source": "格林公式",
    "target": "曲线积分与路径无关",
    "weight": 0.9
  },
  {
    "source": "等比级数求和",
    "target": "幂级数求和函数",
    "weight": 0.85
  },
  {
    "source": "幂级数逐项求导",
    "target": "幂级数求和函数",
    "weight": 0.95
  },
  {
    "source": "向量组的线性相关性",
    "target": "向量组的秩",
    "weight": 0.9
  },
  {
    "source": "定积分的定义",
    "target": "定积分的计算",
    "weight": 0.8
  },
  {
    "source": "分部积分法",
    "target": "定积分的计算",
    "weight": 0.9
  },
  {
    "source": "隐函数求导",
    "target": "隐函数二阶导数",
    "weight": 0.9
  },
  {
    "source": "隐函数求导",
    "target": "求驻点",
    "weight": 0.85
  },
  {
    "source": "隐函数二阶导数",
    "target": "极值的第二充分条件",
    "weight": 0.9
  },
  {
    "source": "求驻点",
    "target": "极值的第二充分条件",
    "weight": 0.85
  },
  {
    "source": "极限的保号性",
    "target": "零点定理",
    "weight": 0.85
  },
  {
    "source": "零点定理",
    "target": "罗尔定理",
    "weight": 0.8
  },
  {
    "source": "极限概念",
    "target": "极限的保号性",
    "weight": 0.9
  },
  {
    "source": "可导性",
    "target": "连续性",
    "weight": 0.95
  },
  {
    "source": "连续性",
    "target": "零点定理",
    "weight": 0.95
  },
  {
    "source": "罗尔定理",
    "target": "构造辅助函数",
    "weight": 0.85
  },
  {
    "source": "空间曲线投影",
    "target": "第一型曲面积分",
    "weight": 0.9
  },
  {
    "source": "第一型曲面积分",
    "target": "曲面质量计算",
    "weight": 0.95
  },
  {
    "source": "二重积分计算",
    "target": "第一型曲面积分",
    "weight": 0.9
  },
  {
    "source": "导数计算",
    "target": "方程根的证明",
    "weight": 0.8
  },
  {
    "source": "向量线性相关",
    "target": "行列式为0",
    "weight": 0.9
  },
  {
    "source": "行列式为0",
    "target": "特征值性质",
    "weight": 0.9
  },
  {
    "source": "特征值互异",
    "target": "矩阵相似对角化",
    "weight": 0.9
  },
  {
    "source": "矩阵相似对角化",
    "target": "矩阵的秩",
    "weight": 0.85
  },
  {
    "source": "矩阵的秩",
    "target": "基础解系",
    "weight": 0.9
  },
  {
    "source": "基础解系",
    "target": "非齐次线性方程组解的结构",
    "weight": 0.95
  },
  {
    "source": "向量的线性表示",
    "target": "齐次线性方程组的基础解系",
    "weight": 0.9
  },
  {
    "source": "向量的线性表示",
    "target": "非齐次线性方程组的特解",
    "weight": 0.9
  },
  {
    "source": "特征值与特征向量",
    "target": "二次型的标准形",
    "weight": 0.95
  },
  {
    "source": "特征值与特征向量",
    "target": "正交矩阵",
    "weight": 0.9
  },
  {
    "source": "正交变换",
    "target": "二次型的标准形",
    "weight": 0.9
  },
  {
    "source": "二次型的矩阵表示",
    "target": "正交变换化标准形",
    "weight": 0.9
  },
  {
    "source": "正交变换化标准形",
    "target": "特征值",
    "weight": 0.95
  },
  {
    "source": "特征值",
    "target": "矩阵的秩",
    "weight": 0.85
  },
  {
    "source": "行列式",
    "target": "行列式的计算",
    "weight": 0.8
  },
  {
    "source": "特征向量",
    "target": "矩阵相似对角化",
    "weight": 0.9
  },
  {
    "source": "特征向量",
    "target": "向量正交化与单位化",
    "weight": 0.85
  },
  {
    "source": "矩阵相似对角化",
    "target": "实对称矩阵正交相似对角化",
    "weight": 0.85
  },
  {
    "source": "向量正交化与单位化",
    "target": "实对称矩阵正交相似对角化",
    "weight": 0.9
  },
  {
    "source": "连续型随机变量的数学期望",
    "target": "连续型随机变量的概率计算",
    "weight": 0.9
  },
  {
    "source": "离散型随机变量的分布律",
    "target": "随机变量和的分布",
    "weight": 0.8
  },
  {
    "source": "连续型随机变量的概率密度",
    "target": "随机变量和的分布",
    "weight": 0.8
  },
  {
    "source": "随机变量的独立性",
    "target": "随机变量和的分布",
    "weight": 0.85
  },
  {
    "source": "全概率公式",
    "target": "随机变量和的分布",
    "weight": 0.75
  },
  {
    "source": "矩阵对角化",
    "target": "二次型的标准形",
    "weight": 0.9
  },
  {
    "source": "全概率公式",
    "target": "连续型与离散型随机变量和的分布",
    "weight": 0.85
  },
  {
    "source": "随机变量的独立性",
    "target": "连续型与离散型随机变量和的分布",
    "weight": 0.85
  },
  {
    "source": "分布函数的定义与性质",
    "target": "连续型与离散型随机变量和的分布",
    "weight": 0.9
  },
  {
    "source": "分布函数的定义与性质",
    "target": "概率密度函数",
    "weight": 0.95
  },
  {
    "source": "分段函数求导",
    "target": "概率密度函数",
    "weight": 0.75
  },
  {
    "source": "正态分布",
    "target": "随机变量函数的分布",
    "weight": 0.9
  },
  {
    "source": "随机变量函数的分布",
    "target": "数学期望",
    "weight": 0.85
  },
  {
    "source": "随机变量函数的分布",
    "target": "最大似然估计",
    "weight": 0.9
  },
  {
    "source": "正态分布",
    "target": "正态分布的概率密度",
    "weight": 0.9
  },
  {
    "source": "正态分布的对称性",
    "target": "概率密度函数的化简",
    "weight": 0.85
  },
  {
    "source": "概率密度函数",
    "target": "连续型随机变量的期望",
    "weight": 0.9
  },
  {
    "source": "定积分的换元法",
    "target": "连续型随机变量的期望",
    "weight": 0.85
  },
  {
    "source": "标准正态分布的性质",
    "target": "连续型随机变量的期望",
    "weight": 0.8
  },
  {
    "source": "数学期望",
    "target": "样本均值",
    "weight": 0.85
  },
  {
    "source": "对数似然函数",
    "target": "极大似然估计",
    "weight": 0.95
  },
  {
    "source": "导数运算",
    "target": "求解方程",
    "weight": 0.85
  },
  {
    "source": "求解方程",
    "target": "最大似然估计",
    "weight": 0.9
  },
  {
    "source": "对数似然函数",
    "target": "最大似然估计",
    "weight": 0.95
  },
  {
    "source": "导数的定义",
    "target": "绝对值函数的导数",
    "weight": 0.9
  },
  {
    "source": "复合函数求导法则",
    "target": "绝对值函数的导数",
    "weight": 0.7
  },
  {
    "source": "偏导数",
    "target": "曲面的切平面方程",
    "weight": 0.9
  },
  {
    "source": "曲面的切平面方程",
    "target": "空间平面方程",
    "weight": 0.85
  },
  {
    "source": "三角函数的麦克劳林展开",
    "target": "幂级数展开",
    "weight": 0.8
  },
  {
    "source": "幂级数展开",
    "target": "常数项级数求和",
    "weight": 0.9
  },
  {
    "source": "定积分的概念与性质",
    "target": "奇偶函数定积分性质",
    "weight": 0.9
  },
  {
    "source": "定积分的概念与性质",
    "target": "定积分的比较定理",
    "weight": 0.9
  },
  {
    "source": "矩阵相似",
    "target": "若尔当标准形",
    "weight": 0.9
  },
  {
    "source": "矩阵的秩",
    "target": "分块矩阵的秩",
    "weight": 0.9
  },
  {
    "source": "概率密度函数",
    "target": "连续型随机变量概率计算",
    "weight": 0.9
  },
  {
    "source": "正态分布",
    "target": "假设检验",
    "weight": 0.85
  },
  {
    "source": "假设检验",
    "target": "显著性水平",
    "weight": 0.9
  },
  {
    "source": "泊松分布",
    "target": "协方差计算",
    "weight": 0.8
  },
  {
    "source": "概率密度函数",
    "target": "极大似然估计",
    "weight": 1.0
  },
  {
    "source": "极大似然估计",
    "target": "数学期望",
    "weight": 0.9
  },
  {
    "source": "极大似然估计",
    "target": "方差",
    "weight": 0.9
  },
  {
    "source": "偏导数",
    "target": "法向量",
    "weight": 0.9
  },
  {
    "source": "法向量",
    "target": "切平面",
    "weight": 1.0
  },
  {
    "source": "泰勒展开",
    "target": "常数项级数求和",
    "weight": 0.9
  },
  {
    "source": "正弦函数的幂级数展开",
    "target": "常数项级数求和",
    "weight": 0.85
  },
  {
    "source": "余弦函数的幂级数展开",
    "target": "常数项级数求和",
    "weight": 0.85
  },
  {
    "source": "定积分的奇偶性",
    "target": "定积分计算",
    "weight": 0.85
  },
  {
    "source": "定积分的比较性质",
    "target": "定积分比较大小",
    "weight": 0.8
  },
  {
    "source": "矩阵的特征值",
    "target": "特征值的几何重数",
    "weight": 0.9
  },
  {
    "source": "矩阵的秩",
    "target": "特征值的几何重数",
    "weight": 0.9
  },
  {
    "source": "函数对称性",
    "target": "对称区间定积分",
    "weight": 0.85
  },
  {
    "source": "标准正态分布分位数",
    "target": "假设检验拒绝域",
    "weight": 0.9
  },
  {
    "source": "定积分分部积分法",
    "target": "含高阶导数的定积分计算",
    "weight": 0.95
  },
  {
    "source": "哈密顿算子",
    "target": "旋度计算",
    "weight": 0.95
  },
  {
    "source": "行列式展开",
    "target": "旋度计算",
    "weight": 0.9
  },
  {
    "source": "空间曲线方程",
    "target": "第一类曲线积分",
    "weight": 0.85
  },
  {
    "source": "轮换对称性",
    "target": "第一类曲线积分",
    "weight": 0.8
  },
  {
    "source": "矩阵乘法",
    "target": "特征值与特征向量性质",
    "weight": 0.85
  },
  {
    "source": "特征值与特征向量定义",
    "target": "特征值与特征向量性质",
    "weight": 0.95
  },
  {
    "source": "特征值与特征向量的定义",
    "target": "特征向量的线性无关性",
    "weight": 0.9
  },
  {
    "source": "特征值与特征向量的定义",
    "target": "特征值与行列式的关系",
    "weight": 0.95
  },
  {
    "source": "特征向量的线性无关性",
    "target": "向量线性组合的系数对应",
    "weight": 0.85
  },
  {
    "source": "特征值与行列式的关系",
    "target": "方阵行列式的计算",
    "weight": 0.9
  },
  {
    "source": "三重积分计算",
    "target": "二重积分计算",
    "weight": 0.8
  },
  {
    "source": "二重积分计算",
    "target": "极坐标变换",
    "weight": 0.8
  },
  {
    "source": "极坐标变换",
    "target": "定积分计算",
    "weight": 0.85
  },
  {
    "source": "常数变易法",
    "target": "一阶线性微分方程的通解",
    "weight": 0.9
  },
  {
    "source": "周期函数",
    "target": "微分方程解的周期性",
    "weight": 0.85
  },
  {
    "source": "一阶线性微分方程",
    "target": "微分方程解的周期性",
    "weight": 0.8
  },
  {
    "source": "导数",
    "target": "函数单调性",
    "weight": 0.95
  },
  {
    "source": "导数判断函数单调性",
    "target": "证明函数不等式",
    "weight": 0.9
  },
  {
    "source": "证明函数不等式",
    "target": "数列单调性判断",
    "weight": 0.85
  },
  {
    "source": "数学归纳法",
    "target": "数列有界性",
    "weight": 0.85
  },
  {
    "source": "数列单调性判断",
    "target": "单调有界准则",
    "weight": 0.9
  },
  {
    "source": "数列有界性",
    "target": "单调有界准则",
    "weight": 0.9
  },
  {
    "source": "单调有界准则",
    "target": "数列极限存在性",
    "weight": 0.95
  },
  {
    "source": "数列极限存在性",
    "target": "求递推数列的极限",
    "weight": 0.9
  },
  {
    "source": "函数零点",
    "target": "求递推数列的极限",
    "weight": 0.8
  },
  {
    "source": "矩阵的秩",
    "target": "矩阵等价",
    "weight": 0.85
  },
  {
    "source": "可逆线性变换",
    "target": "二次型的规范形",
    "weight": 0.85
  },
  {
    "source": "配方法化二次型为标准形",
    "target": "二次型的规范形",
    "weight": 0.9
  },
  {
    "source": "行列式的性质",
    "target": "行列式计算",
    "weight": 0.9
  },
  {
    "source": "行列式计算",
    "target": "参数求解",
    "weight": 0.85
  },
  {
    "source": "增广矩阵",
    "target": "矩阵方程求解",
    "weight": 0.9
  },
  {
    "source": "行列式计算",
    "target": "逆矩阵的判定",
    "weight": 0.9
  },
  {
    "source": "矩阵方程求解",
    "target": "矩阵可逆",
    "weight": 0.85
  },
  {
    "source": "随机变量的独立性",
    "target": "数学期望的性质",
    "weight": 0.85
  },
  {
    "source": "离散型随机变量的概率分布",
    "target": "随机变量函数的分布",
    "weight": 0.85
  },
  {
    "source": "泊松分布",
    "target": "数学期望",
    "weight": 0.8
  },
  {
    "source": "概率密度函数",
    "target": "似然函数构造",
    "weight": 0.9
  },
  {
    "source": "对数似然函数",
    "target": "导数求解",
    "weight": 0.9
  },
  {
    "source": "导数求解",
    "target": "极大似然估计",
    "weight": 0.9
  },
  {
    "source": "数学期望的定义与计算",
    "target": "方差与期望的关系公式",
    "weight": 0.9
  },
  {
    "source": "方差与期望的关系公式",
    "target": "样本均值的方差性质",
    "weight": 0.85
  },
  {
    "source": "含绝对值的定积分计算",
    "target": "数学期望的定义与计算",
    "weight": 0.8
  },
  {
    "source": "样本均值的方差性质",
    "target": "估计量的方差计算",
    "weight": 0.9
  },
  {
    "source": "函数",
    "target": "极限",
    "weight": 0.95
  },
  {
    "source": "极限",
    "target": "连续",
    "weight": 0.95
  },
  {
    "source": "连续",
    "target": "导数与微分",
    "weight": 0.9
  },
  {
    "source": "导数与微分",
    "target": "中值定理与一元函数微分学的应用",
    "weight": 0.95
  },
  {
    "source": "导数与微分",
    "target": "不定积分",
    "weight": 0.85
  },
  {
    "source": "不定积分",
    "target": "定积分及应用",
    "weight": 0.95
  },
  {
    "source": "极限",
    "target": "多元函数微分学",
    "weight": 0.8
  },
  {
    "source": "导数与微分",
    "target": "多元函数微分学",
    "weight": 0.9
  },
  {
    "source": "定积分及应用",
    "target": "二重积分",
    "weight": 0.85
  },
  {
    "source": "多元函数微分学",
    "target": "二重积分",
    "weight": 0.7
  },
  {
    "source": "定积分及应用",
    "target": "微分方程",
    "weight": 0.8
  },
  {
    "source": "导数与微分",
    "target": "微分方程",
    "weight": 0.85
  },
  {
    "source": "二重积分",
    "target": "三重积分与曲线、曲面积分",
    "weight": 0.9
  },
  {
    "source": "极限",
    "target": "无穷级数",
    "weight": 0.9
  },
  {
    "source": "定积分及应用",
    "target": "无穷级数",
    "weight": 0.7
  },
  {
    "source": "向量代数与空间解析几何",
    "target": "三重积分与曲线、曲面积分",
    "weight": 0.8
  },
  {
    "source": "向量代数与空间解析几何",
    "target": "多元函数微分学",
    "weight": 0.6
  },
  {
    "source": "行列式",
    "target": "矩阵",
    "weight": 0.9
  },
  {
    "source": "矩阵",
    "target": "向量",
    "weight": 0.9
  },
  {
    "source": "矩阵",
    "target": "线性方程组",
    "weight": 0.95
  },
  {
    "source": "向量",
    "target": "线性方程组",
    "weight": 0.95
  },
  {
    "source": "行列式",
    "target": "矩阵的特征值和特征向量",
    "weight": 0.7
  },
  {
    "source": "矩阵",
    "target": "矩阵的特征值和特征向量",
    "weight": 0.95
  },
  {
    "source": "向量",
    "target": "矩阵的特征值和特征向量",
    "weight": 0.8
  },
  {
    "source": "矩阵的特征值和特征向量",
    "target": "二次型",
    "weight": 0.95
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  {
    "source": "随机事件与概率",
    "target": "随机变量及其分布",
    "weight": 0.95
  },
  {
    "source": "随机变量及其分布",
    "target": "多维随机变量及其分布",
    "weight": 0.9
  },
  {
    "source": "随机变量及其分布",
    "target": "随机变量的数字特征",
    "weight": 0.9
  },
  {
    "source": "多维随机变量及其分布",
    "target": "随机变量的数字特征",
    "weight": 0.85
  },
  {
    "source": "随机变量的数字特征",
    "target": "大数定律和中心极限定理",
    "weight": 0.9
  },
  {
    "source": "多维随机变量及其分布",
    "target": "数理统计的基本概念",
    "weight": 0.8
  },
  {
    "source": "数理统计的基本概念",
    "target": "参数估计",
    "weight": 0.9
  },
  {
    "source": "参数估计",
    "target": "假设检验",
    "weight": 0.85
  },
  {
    "source": "极限的概念",
    "target": "无穷小的比较",
    "weight": 0.9
  },
  {
    "source": "无穷小的比较",
    "target": "等价无穷小替换",
    "weight": 0.9
  },
  {
    "source": "极限的概念",
    "target": "数列极限",
    "weight": 0.9
  },
  {
    "source": "数列极限",
    "target": "定积分的定义",
    "weight": 0.9
  },
  {
    "source": "极限的概念",
    "target": "左右极限",
    "weight": 0.85
  },
  {
    "source": "左右极限",
    "target": "极限存在准则",
    "weight": 0.85
  },
  {
    "source": "极限的概念与性质",
    "target": "极限的计算",
    "weight": 0.9
  },
  {
    "source": "极限的概念与性质",
    "target": "左右极限",
    "weight": 0.9
  },
  {
    "source": "极限的计算",
    "target": "等价无穷小替换",
    "weight": 0.9
  },
  {
    "source": "极限的计算",
    "target": "泰勒公式",
    "weight": 0.9
  },
  {
    "source": "极限的计算",
    "target": "洛必达法则",
    "weight": 0.9
  },
  {
    "source": "极限的计算",
    "target": "有理化",
    "weight": 0.8
  },
  {
    "source": "等价无穷小替换",
    "target": "泰勒公式",
    "weight": 0.85
  },
  {
    "source": "左右极限",
    "target": "函数的连续性",
    "weight": 0.95
  },
  {
    "source": "极限的计算",
    "target": "函数的连续性",
    "weight": 0.95
  },
  {
    "source": "连续性",
    "target": "间断点",
    "weight": 0.9
  },
  {
    "source": "间断点",
    "target": "间断点分类",
    "weight": 0.85
  },
  {
    "source": "间断点分类",
    "target": "可去间断点",
    "weight": 0.8
  },
  {
    "source": "间断点分类",
    "target": "跳跃间断点",
    "weight": 0.8
  },
  {
    "source": "间断点分类",
    "target": "第二类间断点",
    "weight": 0.8
  },
  {
    "source": "变上限积分函数",
    "target": "连续性",
    "weight": 0.9
  },
  {
    "source": "连续性",
    "target": "连续点",
    "weight": 0.85
  },
  {
    "source": "极限的概念",
    "target": "等价无穷小代换",
    "weight": 0.9
  },
  {
    "source": "泰勒公式",
    "target": "等价无穷小代换",
    "weight": 0.85
  },
  {
    "source": "等价无穷小代换",
    "target": "0/0型极限计算",
    "weight": 0.95
  },
  {
    "source": "泰勒公式",
    "target": "0/0型极限计算",
    "weight": 0.9
  },
  {
    "source": "有理化",
    "target": "0/0型极限计算",
    "weight": 0.85
  },
  {
    "source": "三角函数恒等变换",
    "target": "0/0型极限计算",
    "weight": 0.8
  },
  {
    "source": "复合函数极限",
    "target": "0/0型极限计算",
    "weight": 0.85
  },
  {
    "source": "极限概念",
    "target": "极限计算",
    "weight": 0.95
  },
  {
    "source": "高阶导数",
    "target": "泰勒公式",
    "weight": 1.0
  },
  {
    "source": "等价无穷小",
    "target": "泰勒公式",
    "weight": 0.8
  },
  {
    "source": "极限计算",
    "target": "幂指函数极限",
    "weight": 0.85
  },
  {
    "source": "对数恒等式",
    "target": "幂指函数极限",
    "weight": 0.9
  },
  {
    "source": "反三角函数",
    "target": "极限计算",
    "weight": 0.7
  },
  {
    "source": "极限概念",
    "target": "1^∞型极限",
    "weight": 0.9
  },
  {
    "source": "1^∞型极限",
    "target": "取对数法",
    "weight": 0.95
  },
  {
    "source": "等价无穷小替换",
    "target": "1^∞型极限",
    "weight": 0.85
  },
  {
    "source": "导数概念",
    "target": "导数定义求极限",
    "weight": 0.85
  },
  {
    "source": "导数概念",
    "target": "导数几何意义",
    "weight": 0.9
  },
  {
    "source": "导数几何意义",
    "target": "切线方程",
    "weight": 0.95
  },
  {
    "source": "函数连续性",
    "target": "极限计算",
    "weight": 0.8
  },
  {
    "source": "数列极限",
    "target": "定积分定义",
    "weight": 0.95
  },
  {
    "source": "对数运算",
    "target": "乘积数列极限",
    "weight": 0.85
  },
  {
    "source": "乘积数列极限",
    "target": "定积分定义",
    "weight": 0.9
  },
  {
    "source": "多项式求和",
    "target": "数列极限",
    "weight": 0.8
  },
  {
    "source": "三角函数求和",
    "target": "定积分定义",
    "weight": 0.85
  },
  {
    "source": "定积分的几何意义",
    "target": "定积分等式证明",
    "weight": 0.85
  },
  {
    "source": "连续函数的零点定理",
    "target": "定积分等式证明",
    "weight": 0.9
  },
  {
    "source": "定积分的区间可加性",
    "target": "对称函数的定积分性质",
    "weight": 0.9
  },
  {
    "source": "定积分的分部积分法",
    "target": "含导数的定积分计算",
    "weight": 0.9
  },
  {
    "source": "柯西-施瓦茨不等式",
    "target": "定积分不等式证明",
    "weight": 0.9
  },
  {
    "source": "定积分的换元法",
    "target": "三角函数定积分计算",
    "weight": 0.85
  },
  {
    "source": "三角函数定积分计算",
    "target": "华里士公式",
    "weight": 0.8
  },
  {
    "source": "导数",
    "target": "二阶导数",
    "weight": 1.0
  },
  {
    "source": "函数凹凸性",
    "target": "积分不等式证明",
    "weight": 0.85
  },
  {
    "source": "定积分计算",
    "target": "平面区域面积",
    "weight": 0.95
  },
  {
    "source": "定积分计算",
    "target": "旋转体体积",
    "weight": 0.95
  },
  {
    "source": "旋转体体积(绕x轴)",
    "target": "旋转体体积(绕y轴)",
    "weight": 0.8
  },
  {
    "source": "极限",
    "target": "反常积分",
    "weight": 0.95
  },
  {
    "source": "定积分计算",
    "target": "反常积分",
    "weight": 0.9
  },
  {
    "source": "多元函数偏导数",
    "target": "多元函数可微性",
    "weight": 0.95
  },
  {
    "source": "多元函数极限",
    "target": "多元函数偏导数",
    "weight": 0.9
  },
  {
    "source": "二元函数极限",
    "target": "极限的保号性",
    "weight": 0.85
  },
  {
    "source": "极限的保号性",
    "target": "多元函数极值判定",
    "weight": 0.9
  },
  {
    "source": "二元函数连续性",
    "target": "二元函数偏导数",
    "weight": 0.7
  },
  {
    "source": "二元函数偏导数",
    "target": "二元函数可微性",
    "weight": 0.9
  },
  {
    "source": "二元函数可微性",
    "target": "连续与可偏导及可微的关系",
    "weight": 0.9
  },
  {
    "source": "曲线积分与路径无关",
    "target": "一阶线性微分方程",
    "weight": 0.9
  },
  {
    "source": "一阶线性微分方程",
    "target": "初值问题求解",
    "weight": 0.85
  },
  {
    "source": "格林公式",
    "target": "闭曲线积分计算",
    "weight": 0.9
  },
  {
    "source": "格林公式",
    "target": "挖洞法",
    "weight": 0.85
  },
  {
    "source": "偏导数",
    "target": "面积微元计算",
    "weight": 0.9
  },
  {
    "source": "空间曲面交线及投影域",
    "target": "曲面投影法",
    "weight": 0.85
  },
  {
    "source": "面积微元计算",
    "target": "曲面投影法",
    "weight": 0.9
  },
  {
    "source": "曲面投影法",
    "target": "对面积的曲面积分",
    "weight": 0.95
  },
  {
    "source": "二重积分计算",
    "target": "对面积的曲面积分",
    "weight": 0.9
  },
  {
    "source": "参数化法",
    "target": "对坐标的曲线积分",
    "weight": 0.9
  },
  {
    "source": "曲面的切平面方程",
    "target": "点到平面的距离",
    "weight": 0.85
  },
  {
    "source": "点到平面的距离",
    "target": "第一类曲面积分",
    "weight": 0.8
  },
  {
    "source": "两类曲面积分的关系",
    "target": "第二类曲面积分",
    "weight": 0.85
  },
  {
    "source": "偏导数",
    "target": "高斯公式",
    "weight": 0.95
  },
  {
    "source": "高斯公式",
    "target": "第二类曲面积分",
    "weight": 0.95
  },
  {
    "source": "曲面积分",
    "target": "第二类曲面积分",
    "weight": 0.9
  },
  {
    "source": "第二类曲面积分",
    "target": "曲面侧",
    "weight": 0.85
  },
  {
    "source": "正项级数收敛",
    "target": "绝对收敛",
    "weight": 0.9
  },
  {
    "source": "莱布尼茨判别法",
    "target": "条件收敛",
    "weight": 0.85
  },
  {
    "source": "绝对收敛",
    "target": "条件收敛",
    "weight": 0.8
  },
  {
    "source": "级数收敛的定义",
    "target": "裂项相消法",
    "weight": 0.85
  },
  {
    "source": "级数收敛的定义",
    "target": "正项级数判别法",
    "weight": 0.9
  },
  {
    "source": "正项级数判别法",
    "target": "比较判别法",
    "weight": 0.9
  },
  {
    "source": "正项级数判别法",
    "target": "比值判别法",
    "weight": 0.85
  },
  {
    "source": "正项级数判别法",
    "target": "根值判别法",
    "weight": 0.85
  },
  {
    "source": "级数收敛的定义",
    "target": "绝对收敛与条件收敛",
    "weight": 0.9
  },
  {
    "source": "级数的性质",
    "target": "正项级数判别法",
    "weight": 0.8
  },
  {
    "source": "级数收敛的定义",
    "target": "正项级数判敛法",
    "weight": 0.9
  },
  {
    "source": "级数收敛的定义",
    "target": "交错级数判敛法",
    "weight": 0.9
  },
  {
    "source": "正项级数判敛法",
    "target": "比较判别法",
    "weight": 0.95
  },
  {
    "source": "交错级数判敛法",
    "target": "绝对收敛与条件收敛",
    "weight": 0.85
  },
  {
    "source": "等价无穷小",
    "target": "比较判别法的极限形式",
    "weight": 0.9
  },
  {
    "source": "比较判别法",
    "target": "级数的夹逼准则",
    "weight": 0.85
  },
  {
    "source": "极限概念",
    "target": "比较判别法的极限形式",
    "weight": 0.9
  },
  {
    "source": "正项级数",
    "target": "比较判别法的极限形式",
    "weight": 0.85
  },
  {
    "source": "比较判别法的极限形式",
    "target": "正项级数敛散性",
    "weight": 0.9
  },
  {
    "source": "根值判别法",
    "target": "幂级数收敛半径",
    "weight": 0.95
  },
  {
    "source": "幂级数收敛半径",
    "target": "幂级数收敛域",
    "weight": 1.0
  },
  {
    "source": "交错级数判别法",
    "target": "幂级数收敛域",
    "weight": 0.85
  },
  {
    "source": "逐项求导",
    "target": "幂级数和函数",
    "weight": 0.95
  },
  {
    "source": "逐项积分",
    "target": "幂级数和函数",
    "weight": 0.95
  },
  {
    "source": "等比级数求和",
    "target": "幂级数和函数",
    "weight": 0.9
  },
  {
    "source": "齐次线性方程组",
    "target": "非齐次线性方程组",
    "weight": 0.9
  },
  {
    "source": "线性方程组解的判定",
    "target": "非齐次线性方程组",
    "weight": 0.85
  },
  {
    "source": "伴随矩阵",
    "target": "伴随矩阵的秩",
    "weight": 0.9
  },
  {
    "source": "矩阵的秩",
    "target": "伴随矩阵的秩",
    "weight": 0.85
  },
  {
    "source": "向量组的线性相关性",
    "target": "齐次线性方程组的解",
    "weight": 0.85
  },
  {
    "source": "向量组的线性组合",
    "target": "基础解系",
    "weight": 0.85
  },
  {
    "source": "齐次线性方程组基础解系",
    "target": "非齐次线性方程组通解",
    "weight": 0.9
  },
  {
    "source": "非齐次线性方程组解的性质",
    "target": "非齐次线性方程组通解",
    "weight": 0.85
  },
  {
    "source": "矩阵的初等行变换",
    "target": "线性方程组解的判定",
    "weight": 0.9
  },
  {
    "source": "线性方程组解的判定",
    "target": "线性方程组的求解",
    "weight": 0.85
  },
  {
    "source": "行列式",
    "target": "矩阵可逆",
    "weight": 0.9
  },
  {
    "source": "矩阵可逆",
    "target": "矩阵的逆",
    "weight": 0.9
  },
  {
    "source": "矩阵的逆",
    "target": "矩阵方程",
    "weight": 0.85
  },
  {
    "source": "矩阵的秩",
    "target": "线性方程组有解条件",
    "weight": 0.95
  },
  {
    "source": "线性方程组有解条件",
    "target": "矩阵方程",
    "weight": 0.85
  },
  {
    "source": "特征值",
    "target": "矩阵可逆",
    "weight": 0.85
  },
  {
    "source": "行列式",
    "target": "特征值",
    "weight": 0.8
  },
  {
    "source": "齐次线性方程组",
    "target": "矩阵的秩",
    "weight": 0.85
  },
  {
    "source": "特征多项式",
    "target": "矩阵相似",
    "weight": 0.8
  },
  {
    "source": "特征值与特征向量的概念",
    "target": "伴随矩阵的特征值",
    "weight": 0.85
  },
  {
    "source": "特征值与特征向量的概念",
    "target": "矩阵的迹与特征值的关系",
    "weight": 0.85
  },
  {
    "source": "特征值与特征向量的概念",
    "target": "特征向量的线性组合性质",
    "weight": 0.9
  },
  {
    "source": "齐次线性方程组的基础解系",
    "target": "特征值为0对应的特征向量",
    "weight": 0.9
  },
  {
    "source": "矩阵可逆的充要条件",
    "target": "特征值与矩阵可逆性的关系",
    "weight": 0.9
  },
  {
    "source": "特征值",
    "target": "实对称矩阵",
    "weight": 0.8
  },
  {
    "source": "矩阵合同",
    "target": "实对称矩阵",
    "weight": 0.7
  },
  {
    "source": "相似对角化",
    "target": "正交对角化",
    "weight": 0.9
  },
  {
    "source": "实对称矩阵",
    "target": "正交对角化",
    "weight": 0.9
  },
  {
    "source": "随机事件",
    "target": "事件的关系与运算",
    "weight": 0.9
  },
  {
    "source": "随机事件",
    "target": "概率",
    "weight": 0.9
  },
  {
    "source": "事件的关系与运算",
    "target": "概率",
    "weight": 0.85
  },
  {
    "source": "顺序统计量",
    "target": "事件的表示与转化",
    "weight": 0.9
  },
  {
    "source": "事件的运算",
    "target": "互斥事件",
    "weight": 0.95
  },
  {
    "source": "互斥事件",
    "target": "互斥事件的概率性质",
    "weight": 0.9
  },
  {
    "source": "事件的运算",
    "target": "概率的基本性质",
    "weight": 0.85
  },
  {
    "source": "条件概率",
    "target": "事件的独立性",
    "weight": 0.9
  },
  {
    "source": "事件的独立性",
    "target": "相互独立事件",
    "weight": 0.85
  },
  {
    "source": "互斥事件",
    "target": "对立事件",
    "weight": 0.9
  },
  {
    "source": "事件的运算",
    "target": "条件概率",
    "weight": 0.8
  },
  {
    "source": "条件概率",
    "target": "互斥事件",
    "weight": 0.7
  },
  {
    "source": "事件的关系与运算",
    "target": "概率加法公式",
    "weight": 0.9
  },
  {
    "source": "连续型随机变量",
    "target": "概率密度函数",
    "weight": 0.9
  },
  {
    "source": "连续型随机变量",
    "target": "分布函数",
    "weight": 0.9
  },
  {
    "source": "概率密度函数",
    "target": "分布函数",
    "weight": 0.95
  },
  {
    "source": "随机变量的独立性",
    "target": "独立随机变量的分布函数与密度函数",
    "weight": 0.85
  },
  {
    "source": "概率密度函数",
    "target": "概率计算",
    "weight": 0.95
  },
  {
    "source": "连续型随机变量",
    "target": "正态分布",
    "weight": 0.9
  },
  {
    "source": "概率密度函数",
    "target": "密度函数的对称性",
    "weight": 0.85
  },
  {
    "source": "分布函数",
    "target": "分布函数求参数",
    "weight": 0.85
  },
  {
    "source": "正态分布",
    "target": "正态分布的对称性",
    "weight": 0.85
  },
  {
    "source": "连续型随机变量",
    "target": "均匀分布",
    "weight": 0.9
  },
  {
    "source": "原假设",
    "target": "假设检验",
    "weight": 0.9
  },
  {
    "source": "第一类错误",
    "target": "假设检验",
    "weight": 0.9
  },
  {
    "source": "显著性水平",
    "target": "第一类错误",
    "weight": 0.95
  },
  {
    "source": "假设检验",
    "target": "单正态总体均值检验",
    "weight": 0.9
  },
  {
    "source": "正态分布",
    "target": "单正态总体均值检验",
    "weight": 0.9
  },
  {
    "source": "极限的概念",
    "target": "函数极限",
    "weight": 0.9
  },
  {
    "source": "极限的概念",
    "target": "无穷大与无穷小",
    "weight": 0.9
  },
  {
    "source": "极限的概念",
    "target": "极限的四则运算法则",
    "weight": 0.9
  },
  {
    "source": "无穷大与无穷小",
    "target": "无界与无穷大的关系",
    "weight": 0.85
  },
  {
    "source": "数列极限",
    "target": "极限的四则运算法则",
    "weight": 0.9
  },
  {
    "source": "函数极限",
    "target": "极限的四则运算法则",
    "weight": 0.9
  },
  {
    "source": "极限的概念",
    "target": "等价无穷小替换",
    "weight": 0.9
  },
  {
    "source": "导数的概念",
    "target": "泰勒公式",
    "weight": 0.9
  },
  {
    "source": "变限积分求导",
    "target": "变限积分的泰勒展开",
    "weight": 0.85
  },
  {
    "source": "泰勒公式",
    "target": "极限存在且非零的条件",
    "weight": 0.9
  },
  {
    "source": "极限概念",
    "target": "无穷小比较",
    "weight": 0.95
  },
  {
    "source": "连续性",
    "target": "间断点分类",
    "weight": 0.9
  },
  {
    "source": "导数概念",
    "target": "泰勒公式",
    "weight": 0.9
  },
  {
    "source": "等价无穷小替换",
    "target": "无穷小比较",
    "weight": 0.85
  },
  {
    "source": "连续性",
    "target": "绝对值函数的连续性",
    "weight": 0.8
  },
  {
    "source": "数列极限",
    "target": "间断点及其分类",
    "weight": 0.85
  },
  {
    "source": "函数极限",
    "target": "间断点及其分类",
    "weight": 0.9
  },
  {
    "source": "极限的概念",
    "target": "极限的计算",
    "weight": 0.9
  },
  {
    "source": "极限的概念",
    "target": "洛必达法则",
    "weight": 0.9
  },
  {
    "source": "导数的定义",
    "target": "洛必达法则",
    "weight": 0.95
  },
  {
    "source": "洛必达法则",
    "target": "极限的计算",
    "weight": 0.9
  },
  {
    "source": "等价无穷小替换",
    "target": "极限的计算",
    "weight": 0.9
  },
  {
    "source": "泰勒公式",
    "target": "极限的计算",
    "weight": 0.95
  },
  {
    "source": "基本初等函数的泰勒展开",
    "target": "泰勒公式",
    "weight": 0.9
  },
  {
    "source": "定积分的概念",
    "target": "积分变限函数",
    "weight": 0.9
  },
  {
    "source": "复合函数求导法则",
    "target": "积分变限函数求导",
    "weight": 0.9
  },
  {
    "source": "原函数",
    "target": "积分变限函数求导",
    "weight": 0.85
  },
  {
    "source": "积分变限函数求导",
    "target": "洛必达法则",
    "weight": 0.85
  },
  {
    "source": "左右极限",
    "target": "极限的计算",
    "weight": 0.8
  },
  {
    "source": "函数的连续性",
    "target": "极限的概念",
    "weight": 0.8
  },
  {
    "source": "函数的周期性",
    "target": "极限的计算",
    "weight": 0.6
  },
  {
    "source": "导数",
    "target": "微分",
    "weight": 0.85
  },
  {
    "source": "函数单调性",
    "target": "连续性",
    "weight": 0.8
  },
  {
    "source": "连续性",
    "target": "间断点及分类",
    "weight": 0.95
  },
  {
    "source": "数列极限",
    "target": "递推数列",
    "weight": 0.85
  },
  {
    "source": "递推数列",
    "target": "单调有界准则",
    "weight": 0.9
  },
  {
    "source": "导数",
    "target": "数列收敛",
    "weight": 0.7
  },
  {
    "source": "数列收敛",
    "target": "不动点方程",
    "weight": 0.85
  },
  {
    "source": "间断点",
    "target": "间断点类型判断",
    "weight": 0.95
  },
  {
    "source": "极限",
    "target": "间断点类型判断",
    "weight": 0.9
  },
  {
    "source": "连续性",
    "target": "可导",
    "weight": 0.9
  },
  {
    "source": "极限",
    "target": "导数概念",
    "weight": 0.95
  },
  {
    "source": "导数概念",
    "target": "可导的充要条件",
    "weight": 0.9
  },
  {
    "source": "极限",
    "target": "导数",
    "weight": 0.9
  },
  {
    "source": "导数",
    "target": "复合函数求导",
    "weight": 0.9
  },
  {
    "source": "左右极限",
    "target": "分段函数连续性",
    "weight": 0.85
  },
  {
    "source": "定积分",
    "target": "变上限积分",
    "weight": 0.9
  },
  {
    "source": "连续性",
    "target": "变上限积分求导",
    "weight": 0.85
  },
  {
    "source": "奇偶函数",
    "target": "变上限积分奇偶性",
    "weight": 0.85
  },
  {
    "source": "定积分的概念与性质",
    "target": "定积分的几何应用",
    "weight": 0.85
  },
  {
    "source": "导数的几何意义",
    "target": "定积分的几何应用",
    "weight": 0.8
  },
  {
    "source": "定积分的概念与性质",
    "target": "反常积分的概念",
    "weight": 0.9
  },
  {
    "source": "反常积分的概念",
    "target": "反常积分的敛散性判别",
    "weight": 0.9
  },
  {
    "source": "三角函数",
    "target": "换元积分法",
    "weight": 0.8
  },
  {
    "source": "复合函数",
    "target": "换元积分法",
    "weight": 0.85
  },
  {
    "source": "换元积分法",
    "target": "定积分的计算",
    "weight": 0.9
  },
  {
    "source": "不定积分",
    "target": "定积分的计算",
    "weight": 0.9
  },
  {
    "source": "复合函数",
    "target": "函数表达式求解",
    "weight": 0.85
  },
  {
    "source": "函数单调性",
    "target": "积分不等式证明",
    "weight": 0.9
  },
  {
    "source": "定积分的性质",
    "target": "积分不等式证明",
    "weight": 0.85
  },
  {
    "source": "定积分的概念",
    "target": "定积分的黎曼和",
    "weight": 0.9
  },
  {
    "source": "拉格朗日中值定理",
    "target": "积分误差估计",
    "weight": 0.85
  },
  {
    "source": "导数连续性",
    "target": "拉格朗日中值定理",
    "weight": 0.8
  },
  {
    "source": "辅助函数构造",
    "target": "积分不等式证明",
    "weight": 0.8
  },
  {
    "source": "定积分",
    "target": "微积分基本定理",
    "weight": 0.9
  },
  {
    "source": "导数",
    "target": "微积分基本定理",
    "weight": 0.9
  },
  {
    "source": "微积分基本定理",
    "target": "积分不等式证明",
    "weight": 0.85
  },
  {
    "source": "柯西-施瓦茨不等式",
    "target": "积分不等式证明",
    "weight": 0.9
  },
  {
    "source": "拉格朗日中值定理",
    "target": "积分不等式证明",
    "weight": 0.8
  },
  {
    "source": "泰勒公式",
    "target": "积分不等式证明",
    "weight": 0.85
  },
  {
    "source": "二阶导数",
    "target": "泰勒公式",
    "weight": 0.85
  },
  {
    "source": "齐次微分方程",
    "target": "一阶线性微分方程",
    "weight": 0.5
  },
  {
    "source": "一阶线性微分方程",
    "target": "可降阶的高阶微分方程",
    "weight": 0.8
  },
  {
    "source": "齐次微分方程",
    "target": "可降阶的高阶微分方程",
    "weight": 0.6
  },
  {
    "source": "一阶线性微分方程",
    "target": "高阶线性微分方程解的结构",
    "weight": 0.9
  },
  {
    "source": "可降阶的高阶微分方程",
    "target": "高阶线性微分方程解的结构",
    "weight": 0.7
  },
  {
    "source": "常系数齐次线性微分方程",
    "target": "常系数非齐次线性微分方程",
    "weight": 0.95
  },
  {
    "source": "常系数非齐次线性微分方程",
    "target": "欧拉方程",
    "weight": 0.85
  },
  {
    "source": "函数",
    "target": "极限与连续",
    "weight": 0.9
  },
  {
    "source": "极限与连续",
    "target": "微分方程的幂级数解法",
    "weight": 0.75
  },
  {
    "source": "函数的概念",
    "target": "函数的主要性质",
    "weight": 1.0
  },
  {
    "source": "函数的概念",
    "target": "有界性",
    "weight": 0.9
  },
  {
    "source": "函数的概念",
    "target": "单调性",
    "weight": 0.9
  },
  {
    "source": "函数定义域",
    "target": "奇偶性",
    "weight": 0.8
  },
  {
    "source": "奇偶性",
    "target": "偶函数",
    "weight": 0.9
  },
  {
    "source": "奇偶性",
    "target": "奇函数",
    "weight": 0.9
  },
  {
    "source": "基本初等函数",
    "target": "初等函数",
    "weight": 1.0
  },
  {
    "source": "常数函数",
    "target": "基本初等函数",
    "weight": 0.8
  },
  {
    "source": "幂函数",
    "target": "基本初等函数",
    "weight": 0.8
  },
  {
    "source": "指数函数",
    "target": "基本初等函数",
    "weight": 0.8
  },
  {
    "source": "对数函数",
    "target": "基本初等函数",
    "weight": 0.8
  },
  {
    "source": "三角函数",
    "target": "基本初等函数",
    "weight": 0.8
  },
  {
    "source": "反三角函数",
    "target": "基本初等函数",
    "weight": 0.8
  },
  {
    "source": "指数函数",
    "target": "指数函数单调性",
    "weight": 0.9
  },
  {
    "source": "指数函数单调性",
    "target": "求一元函数的定义域",
    "weight": 0.85
  },
  {
    "source": "不等式求解",
    "target": "函数定义域",
    "weight": 0.9
  },
  {
    "source": "函数",
    "target": "函数定义域",
    "weight": 0.95
  },
  {
    "source": "函数",
    "target": "复合函数",
    "weight": 0.85
  },
  {
    "source": "函数",
    "target": "函数方程",
    "weight": 0.8
  },
  {
    "source": "代数方程求解",
    "target": "函数方程",
    "weight": 0.8
  },
  {
    "source": "复合函数",
    "target": "数学归纳法",
    "weight": 0.75
  },
  {
    "source": "复合函数",
    "target": "递推关系",
    "weight": 0.9
  },
  {
    "source": "递推关系",
    "target": "数学归纳法",
    "weight": 0.85
  },
  {
    "source": "二项式定理",
    "target": "赋值法",
    "weight": 0.85
  },
  {
    "source": "赋值法",
    "target": "求多项式系数和",
    "weight": 0.9
  },
  {
    "source": "二项式定理",
    "target": "比较系数法",
    "weight": 0.8
  },
  {
    "source": "复合函数",
    "target": "换元法",
    "weight": 0.85
  },
  {
    "source": "对数函数",
    "target": "换元法",
    "weight": 0.8
  },
  {
    "source": "换元法",
    "target": "一元二次方程求解",
    "weight": 0.75
  },
  {
    "source": "极限概念",
    "target": "数列极限",
    "weight": 0.85
  },
  {
    "source": "极限概念",
    "target": "函数极限",
    "weight": 0.85
  },
  {
    "source": "极限概念",
    "target": "无穷小与无穷大",
    "weight": 0.85
  },
  {
    "source": "无穷小与无穷大",
    "target": "无穷小的比较",
    "weight": 0.9
  },
  {
    "source": "无穷小的比较",
    "target": "等价无穷小代换",
    "weight": 0.9
  },
  {
    "source": "连续性",
    "target": "闭区间连续函数性质",
    "weight": 0.85
  },
  {
    "source": "连续性",
    "target": "导数概念",
    "weight": 0.9
  },
  {
    "source": "导数概念",
    "target": "导数基本公式与法则",
    "weight": 0.9
  },
  {
    "source": "导数概念",
    "target": "高阶导数",
    "weight": 0.85
  },
  {
    "source": "导数基本公式与法则",
    "target": "复合函数求导",
    "weight": 0.9
  },
  {
    "source": "导数基本公式与法则",
    "target": "隐函数求导",
    "weight": 0.85
  },
  {
    "source": "导数基本公式与法则",
    "target": "参数方程求导",
    "weight": 0.85
  },
  {
    "source": "导数概念",
    "target": "微分中值定理",
    "weight": 0.85
  },
  {
    "source": "微分中值定理",
    "target": "洛必达法则",
    "weight": 0.85
  },
  {
    "source": "微分中值定理",
    "target": "泰勒公式",
    "weight": 0.85
  },
  {
    "source": "导数概念",
    "target": "函数单调性与凹凸性",
    "weight": 0.85
  },
  {
    "source": "函数单调性与凹凸性",
    "target": "函数的极值与最值",
    "weight": 0.9
  },
  {
    "source": "函数单调性与凹凸性",
    "target": "函数图形描绘",
    "weight": 0.85
  },
  {
    "source": "导数",
    "target": "原函数",
    "weight": 0.9
  },
  {
    "source": "原函数",
    "target": "不定积分",
    "weight": 0.95
  },
  {
    "source": "不定积分",
    "target": "不定积分的基本性质",
    "weight": 0.9
  },
  {
    "source": "导数",
    "target": "不定积分的基本性质",
    "weight": 0.85
  },
  {
    "source": "原函数概念",
    "target": "不定积分基本公式",
    "weight": 0.95
  },
  {
    "source": "基本导数公式",
    "target": "不定积分基本公式",
    "weight": 0.95
  },
  {
    "source": "幂函数积分",
    "target": "有理函数积分",
    "weight": 0.8
  },
  {
    "source": "倒数函数积分",
    "target": "有理函数积分",
    "weight": 0.8
  },
  {
    "source": "基本三角函数积分",
    "target": "复杂三角函数积分",
    "weight": 0.85
  },
  {
    "source": "凑微分法",
    "target": "复杂三角函数积分",
    "weight": 0.85
  },
  {
    "source": "凑微分法",
    "target": "含根式的积分",
    "weight": 0.85
  },
  {
    "source": "倒数函数积分",
    "target": "复杂三角函数积分",
    "weight": 0.7
  },
  {
    "source": "导数概念",
    "target": "原函数概念",
    "weight": 1.0
  },
  {
    "source": "原函数概念",
    "target": "不定积分概念",
    "weight": 0.95
  },
  {
    "source": "求导法则",
    "target": "原函数的验证",
    "weight": 0.85
  },
  {
    "source": "不定积分概念",
    "target": "不定积分计算",
    "weight": 0.8
  },
  {
    "source": "基本积分表",
    "target": "不定积分",
    "weight": 0.85
  },
  {
    "source": "导数",
    "target": "不定积分",
    "weight": 0.9
  },
  {
    "source": "导数概念",
    "target": "原函数",
    "weight": 0.9
  },
  {
    "source": "原函数",
    "target": "原函数的性质",
    "weight": 0.9
  },
  {
    "source": "导数概念",
    "target": "不定积分与导数的关系",
    "weight": 0.9
  },
  {
    "source": "原函数",
    "target": "不定积分与导数的关系",
    "weight": 0.9
  },
  {
    "source": "不定积分",
    "target": "基本积分公式",
    "weight": 0.85
  },
  {
    "source": "不定积分",
    "target": "确定积分常数",
    "weight": 0.85
  },
  {
    "source": "求导运算",
    "target": "原函数概念",
    "weight": 0.9
  },
  {
    "source": "不定积分概念",
    "target": "不定积分性质",
    "weight": 0.9
  },
  {
    "source": "基本求导法则",
    "target": "复合函数求导法则",
    "weight": 0.85
  },
  {
    "source": "原函数概念",
    "target": "求被积函数",
    "weight": 0.85
  },
  {
    "source": "复合函数求导法则",
    "target": "求被积函数",
    "weight": 0.8
  },
  {
    "source": "三角函数恒等式",
    "target": "复合函数求导",
    "weight": 0.75
  },
  {
    "source": "不定积分",
    "target": "初值问题求特解",
    "weight": 0.85
  },
  {
    "source": "代数恒等变形",
    "target": "基本积分公式",
    "weight": 0.8
  },
  {
    "source": "三角恒等变形",
    "target": "基本积分公式",
    "weight": 0.8
  },
  {
    "source": "基本积分公式",
    "target": "不定积分的计算",
    "weight": 0.9
  },
  {
    "source": "导数的几何意义",
    "target": "不定积分的几何意义",
    "weight": 0.9
  },
  {
    "source": "不定积分的概念",
    "target": "初始条件求特解",
    "weight": 0.85
  },
  {
    "source": "原函数",
    "target": "积分曲线",
    "weight": 0.9
  },
  {
    "source": "不定积分",
    "target": "原函数",
    "weight": 0.95
  },
  {
    "source": "初始条件",
    "target": "积分曲线",
    "weight": 0.85
  },
  {
    "source": "不定积分",
    "target": "换元积分法",
    "weight": 0.9
  },
  {
    "source": "换元积分法",
    "target": "第一换元法",
    "weight": 1.0
  },
  {
    "source": "换元积分法",
    "target": "第二换元法",
    "weight": 1.0
  },
  {
    "source": "复合函数求导",
    "target": "第一换元法",
    "weight": 0.9
  },
  {
    "source": "反函数",
    "target": "第二换元法",
    "weight": 0.85
  },
  {
    "source": "不定积分",
    "target": "凑微分法",
    "weight": 0.9
  },
  {
    "source": "凑微分法",
    "target": "复合函数积分",
    "weight": 0.85
  },
  {
    "source": "导数与微分",
    "target": "分部积分法",
    "weight": 0.95
  },
  {
    "source": "原函数概念",
    "target": "分部积分法",
    "weight": 0.85
  },
  {
    "source": "三角恒等式",
    "target": "三角换元法",
    "weight": 0.9
  },
  {
    "source": "基本积分公式",
    "target": "三角换元法",
    "weight": 0.85
  },
  {
    "source": "凑微分法",
    "target": "倒代换法",
    "weight": 0.75
  },
  {
    "source": "不定积分",
    "target": "分部积分法",
    "weight": 0.9
  },
  {
    "source": "导数",
    "target": "分部积分法",
    "weight": 0.9
  },
  {
    "source": "复合函数求导",
    "target": "分部积分法",
    "weight": 0.9
  },
  {
    "source": "凑微分法",
    "target": "分部积分法",
    "weight": 0.9
  },
  {
    "source": "分部积分法",
    "target": "对数函数积分",
    "weight": 0.9
  },
  {
    "source": "不定积分基本公式",
    "target": "凑微分法",
    "weight": 0.9
  },
  {
    "source": "导数与微分运算",
    "target": "凑微分法",
    "weight": 0.85
  },
  {
    "source": "不定积分基本公式",
    "target": "分部积分法",
    "weight": 0.9
  },
  {
    "source": "分部积分法",
    "target": "反三角函数积分",
    "weight": 0.9
  },
  {
    "source": "反三角函数求导",
    "target": "分部积分法",
    "weight": 0.85
  },
  {
    "source": "导数与微分",
    "target": "凑微分法",
    "weight": 0.95
  },
  {
    "source": "不定积分",
    "target": "换元法",
    "weight": 0.85
  },
  {
    "source": "三角恒等变换",
    "target": "三角函数积分",
    "weight": 0.85
  },
  {
    "source": "代数式拆项",
    "target": "有理函数积分",
    "weight": 0.8
  },
  {
    "source": "基本积分公式",
    "target": "凑微分法",
    "weight": 0.9
  },
  {
    "source": "复合函数求导法则",
    "target": "分部积分法",
    "weight": 0.9
  },
  {
    "source": "三角函数恒等变换",
    "target": "不定积分计算",
    "weight": 0.8
  },
  {
    "source": "分部积分法",
    "target": "不定积分计算",
    "weight": 0.95
  },
  {
    "source": "复合函数求导",
    "target": "换元积分法",
    "weight": 0.9
  },
  {
    "source": "不定积分概念",
    "target": "换元积分法",
    "weight": 0.8
  },
  {
    "source": "不定积分概念",
    "target": "分部积分法",
    "weight": 0.8
  },
  {
    "source": "分部积分法",
    "target": "对数函数的积分",
    "weight": 0.9
  },
  {
    "source": "分部积分法",
    "target": "反三角函数的积分",
    "weight": 0.9
  },
  {
    "source": "换元积分法",
    "target": "反三角函数的积分",
    "weight": 0.8
  },
  {
    "source": "换元积分法",
    "target": "有理函数的积分",
    "weight": 0.7
  },
  {
    "source": "假分式化真分式",
    "target": "有理函数的积分",
    "weight": 0.9
  },
  {
    "source": "待定系数法",
    "target": "有理函数的积分",
    "weight": 0.9
  },
  {
    "source": "配方法",
    "target": "有理函数的积分",
    "weight": 0.8
  },
  {
    "source": "分部积分法",
    "target": "有理函数的积分",
    "weight": 0.7
  },
  {
    "source": "有理函数的积分",
    "target": "三角函数有理式的积分",
    "weight": 0.85
  },
  {
    "source": "半角代换",
    "target": "三角函数有理式的积分",
    "weight": 0.9
  },
  {
    "source": "凑微分法",
    "target": "三角函数有理式的积分",
    "weight": 0.8
  },
  {
    "source": "三角恒等变换",
    "target": "三角函数有理式的积分",
    "weight": 0.85
  },
  {
    "source": "倍角公式",
    "target": "三角恒等变换",
    "weight": 0.85
  },
  {
    "source": "积化和差",
    "target": "三角恒等变换",
    "weight": 0.85
  },
  {
    "source": "分部积分法",
    "target": "三角函数乘方的积分",
    "weight": 0.9
  },
  {
    "source": "三角函数乘方的积分",
    "target": "递推公式",
    "weight": 0.85
  },
  {
    "source": "变量代换",
    "target": "简单无理函数的积分",
    "weight": 0.95
  },
  {
    "source": "简单无理函数的积分",
    "target": "有理函数的积分",
    "weight": 0.9
  },
  {
    "source": "有理假分式",
    "target": "有理真分式",
    "weight": 0.85
  },
  {
    "source": "部分分式分解",
    "target": "有理真分式的积分",
    "weight": 0.95
  },
  {
    "source": "有理真分式",
    "target": "有理函数的积分",
    "weight": 0.9
  },
  {
    "source": "多项式积分",
    "target": "有理函数的积分",
    "weight": 0.8
  },
  {
    "source": "换元积分法",
    "target": "根式代换",
    "weight": 0.85
  },
  {
    "source": "根式代换",
    "target": "有理函数积分",
    "weight": 0.8
  },
  {
    "source": "函数表达式求解",
    "target": "不定积分",
    "weight": 0.75
  },
  {
    "source": "对数运算",
    "target": "求解函数方程",
    "weight": 0.8
  },
  {
    "source": "代数化简",
    "target": "有理函数积分",
    "weight": 0.75
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  {
    "source": "基本积分公式",
    "target": "第一换元法",
    "weight": 0.9
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  {
    "source": "第一换元法",
    "target": "有理函数积分",
    "weight": 0.85
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  {
    "source": "第一换元法",
    "target": "无理函数积分",
    "weight": 0.9
  },
  {
    "source": "有理函数积分",
    "target": "无理函数积分",
    "weight": 0.6
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  {
    "source": "凑微分法",
    "target": "三角换元法",
    "weight": 0.85
  },
  {
    "source": "三角函数恒等变换",
    "target": "三角换元法",
    "weight": 0.9
  },
  {
    "source": "三角函数恒等变换",
    "target": "万能换元法",
    "weight": 0.9
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  {
    "source": "函数求导与微分",
    "target": "分部积分法",
    "weight": 0.9
  },
  {
    "source": "反三角函数求导",
    "target": "凑微分法",
    "weight": 0.85
  },
  {
    "source": "基本求导公式",
    "target": "分部积分法",
    "weight": 0.9
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  {
    "source": "基本积分公式",
    "target": "换元积分法",
    "weight": 0.85
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  {
    "source": "三角恒等变换",
    "target": "换元积分法",
    "weight": 0.8
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  {
    "source": "换元积分法",
    "target": "分部积分法",
    "weight": 0.85
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  {
    "source": "不定积分",
    "target": "定积分的概念",
    "weight": 0.8
  },
  {
    "source": "极限",
    "target": "定积分定义",
    "weight": 0.95
  },
  {
    "source": "有界函数",
    "target": "定积分定义",
    "weight": 0.8
  },
  {
    "source": "黎曼和",
    "target": "定积分定义",
    "weight": 0.9
  },
  {
    "source": "定积分定义",
    "target": "可积",
    "weight": 0.9
  },
  {
    "source": "定积分定义",
    "target": "定积分求极限",
    "weight": 0.85
  },
  {
    "source": "和式极限",
    "target": "定积分的定义",
    "weight": 0.9
  },
  {
    "source": "定积分的定义",
    "target": "定积分的基本性质",
    "weight": 0.95
  },
  {
    "source": "定积分的定义",
    "target": "定积分的线性性质",
    "weight": 0.85
  },
  {
    "source": "定积分的定义",
    "target": "定积分的区间可加性",
    "weight": 0.85
  },
  {
    "source": "定积分的定义",
    "target": "定积分上下限的性质",
    "weight": 0.85
  },
  {
    "source": "定积分上下限相同为零",
    "target": "交换积分上下限变号",
    "weight": 0.8
  },
  {
    "source": "可积性",
    "target": "定积分的概念",
    "weight": 0.9
  },
  {
    "source": "定积分的概念",
    "target": "定积分的性质",
    "weight": 0.9
  },
  {
    "source": "定积分的性质",
    "target": "定积分的比较性质",
    "weight": 0.85
  },
  {
    "source": "不定积分公式",
    "target": "定积分的计算",
    "weight": 0.85
  },
  {
    "source": "定积分的概念",
    "target": "定积分方程求解",
    "weight": 0.8
  },
  {
    "source": "定积分的计算",
    "target": "定积分方程求解",
    "weight": 0.85
  },
  {
    "source": "定积分的性质",
    "target": "积分方程求解",
    "weight": 0.9
  },
  {
    "source": "定积分的计算",
    "target": "积分方程求解",
    "weight": 0.95
  },
  {
    "source": "解代数方程组",
    "target": "积分方程求解",
    "weight": 0.9
  },
  {
    "source": "极限的性质",
    "target": "洛必达法则",
    "weight": 0.8
  },
  {
    "source": "定积分换元法",
    "target": "变限积分求导",
    "weight": 0.85
  },
  {
    "source": "洛必达法则",
    "target": "等价无穷小替换",
    "weight": 0.85
  },
  {
    "source": "积分中值定理",
    "target": "极限的计算",
    "weight": 0.8
  },
  {
    "source": "无穷小量",
    "target": "无穷小量的比较",
    "weight": 0.9
  },
  {
    "source": "定积分",
    "target": "变限积分求导",
    "weight": 0.9
  },
  {
    "source": "定积分",
    "target": "分部积分法",
    "weight": 0.9
  },
  {
    "source": "连续导数",
    "target": "分部积分法",
    "weight": 0.7
  },
  {
    "source": "定积分",
    "target": "对称区间定积分性质",
    "weight": 0.9
  },
  {
    "source": "奇函数与偶函数",
    "target": "对称区间定积分性质",
    "weight": 0.9
  },
  {
    "source": "定积分换元法",
    "target": "对称区间定积分性质",
    "weight": 0.85
  },
  {
    "source": "定积分",
    "target": "三角函数定积分性质",
    "weight": 0.85
  },
  {
    "source": "定积分换元法",
    "target": "三角函数定积分性质",
    "weight": 0.8
  },
  {
    "source": "周期函数",
    "target": "周期函数定积分性质",
    "weight": 0.9
  },
  {
    "source": "定积分",
    "target": "周期函数定积分性质",
    "weight": 0.85
  },
  {
    "source": "三角函数定积分性质",
    "target": "华里士公式",
    "weight": 0.8
  },
  {
    "source": "定积分",
    "target": "华里士公式",
    "weight": 0.85
  },
  {
    "source": "定积分的概念与性质",
    "target": "定积分的换元法",
    "weight": 0.9
  },
  {
    "source": "不定积分的换元法",
    "target": "定积分的换元法",
    "weight": 0.85
  },
  {
    "source": "定积分的换元法",
    "target": "分段函数的定积分",
    "weight": 0.8
  },
  {
    "source": "定积分的换元法",
    "target": "凑微分法计算定积分",
    "weight": 0.85
  },
  {
    "source": "定积分的概念",
    "target": "定积分的换元法",
    "weight": 0.9
  },
  {
    "source": "定积分的换元法",
    "target": "定积分的计算",
    "weight": 0.9
  },
  {
    "source": "定积分的换元法",
    "target": "积分变量与参数的区分",
    "weight": 0.85
  },
  {
    "source": "定积分换元法",
    "target": "根式换元",
    "weight": 0.9
  },
  {
    "source": "定积分换元法",
    "target": "三角换元",
    "weight": 0.9
  },
  {
    "source": "多项式除法",
    "target": "有理函数积分",
    "weight": 0.85
  },
  {
    "source": "华里士公式",
    "target": "三角函数定积分",
    "weight": 0.9
  },
  {
    "source": "定积分换元法",
    "target": "定积分计算",
    "weight": 0.95
  },
  {
    "source": "基本积分公式",
    "target": "牛顿-莱布尼茨公式",
    "weight": 0.95
  },
  {
    "source": "代数配方",
    "target": "三角换元法",
    "weight": 0.8
  },
  {
    "source": "三角换元法",
    "target": "定积分换元法",
    "weight": 0.9
  },
  {
    "source": "三角函数降幂公式",
    "target": "定积分计算",
    "weight": 0.8
  },
  {
    "source": "定积分的几何意义",
    "target": "定积分计算",
    "weight": 0.9
  },
  {
    "source": "定积分分部积分法",
    "target": "定积分计算",
    "weight": 0.9
  },
  {
    "source": "根式代换",
    "target": "换元积分法",
    "weight": 0.85
  },
  {
    "source": "基本积分公式",
    "target": "定积分计算",
    "weight": 0.9
  },
  {
    "source": "反三角函数的积分",
    "target": "基本积分公式",
    "weight": 0.8
  },
  {
    "source": "凑微分法",
    "target": "定积分换元法",
    "weight": 0.9
  },
  {
    "source": "定积分换元法",
    "target": "幂函数定积分",
    "weight": 0.85
  },
  {
    "source": "幂函数定积分",
    "target": "代数方程求解",
    "weight": 0.8
  },
  {
    "source": "定积分基本性质",
    "target": "积分变量无关性",
    "weight": 0.95
  },
  {
    "source": "定积分的区间可加性",
    "target": "定积分的换元法",
    "weight": 0.8
  },
  {
    "source": "定积分的换元法",
    "target": "定积分的比较性质",
    "weight": 0.85
  },
  {
    "source": "三角函数的性质",
    "target": "定积分的比较性质",
    "weight": 0.9
  },
  {
    "source": "定积分的换元法",
    "target": "区间再现公式",
    "weight": 0.9
  },
  {
    "source": "区间再现公式",
    "target": "相加抵消法求定积分",
    "weight": 0.95
  },
  {
    "source": "三角函数诱导公式",
    "target": "三角函数定积分计算",
    "weight": 0.85
  },
  {
    "source": "三角函数定积分计算",
    "target": "相加抵消法求定积分",
    "weight": 0.8
  },
  {
    "source": "定积分",
    "target": "定积分的换元法",
    "weight": 0.9
  },
  {
    "source": "定积分",
    "target": "定积分的分部积分法",
    "weight": 0.9
  },
  {
    "source": "定积分的换元法",
    "target": "对称区间定积分计算",
    "weight": 0.85
  },
  {
    "source": "定积分的分部积分法",
    "target": "多项式与对数乘积的定积分",
    "weight": 0.85
  },
  {
    "source": "复合函数",
    "target": "定积分换元法",
    "weight": 0.85
  },
  {
    "source": "定积分换元法",
    "target": "分部积分法",
    "weight": 0.8
  },
  {
    "source": "导数乘法法则",
    "target": "分部积分法",
    "weight": 0.9
  },
  {
    "source": "分部积分法",
    "target": "牛顿-莱布尼茨公式",
    "weight": 0.85
  },
  {
    "source": "原函数的概念",
    "target": "变限积分求导",
    "weight": 0.85
  },
  {
    "source": "原函数的概念",
    "target": "牛顿-莱布尼茨公式",
    "weight": 0.9
  },
  {
    "source": "变限积分求导",
    "target": "定积分的分部积分法",
    "weight": 0.85
  },
  {
    "source": "导数的四则运算",
    "target": "定积分的分部积分法",
    "weight": 0.8
  },
  {
    "source": "定积分",
    "target": "变限积分",
    "weight": 0.9
  },
  {
    "source": "变限积分",
    "target": "积分不等式证明",
    "weight": 0.85
  },
  {
    "source": "极限",
    "target": "广义积分概念",
    "weight": 0.95
  },
  {
    "source": "定积分",
    "target": "广义积分概念",
    "weight": 0.95
  },
  {
    "source": "广义积分概念",
    "target": "无穷区间上的广义积分",
    "weight": 0.9
  },
  {
    "source": "广义积分概念",
    "target": "瑕积分",
    "weight": 0.9
  },
  {
    "source": "广义积分概念",
    "target": "广义积分计算",
    "weight": 0.9
  },
  {
    "source": "换元积分法",
    "target": "广义积分计算",
    "weight": 0.85
  },
  {
    "source": "凑微分法",
    "target": "广义积分计算",
    "weight": 0.85
  },
  {
    "source": "广义积分概念",
    "target": "广义积分敛散性判定",
    "weight": 0.9
  },
  {
    "source": "定积分的可加性",
    "target": "绝对值函数的积分",
    "weight": 0.9
  },
  {
    "source": "基本积分公式",
    "target": "反常积分计算",
    "weight": 0.85
  },
  {
    "source": "反常积分",
    "target": "反常积分的敛散性",
    "weight": 0.9
  },
  {
    "source": "绝对值函数的积分",
    "target": "含绝对值的反常积分计算",
    "weight": 0.85
  },
  {
    "source": "配方法",
    "target": "基本积分公式",
    "weight": 0.8
  },
  {
    "source": "极限运算",
    "target": "反常积分计算",
    "weight": 0.9
  },
  {
    "source": "定积分计算",
    "target": "反常积分计算",
    "weight": 0.95
  },
  {
    "source": "二元函数极限",
    "target": "二元函数连续",
    "weight": 0.9
  },
  {
    "source": "偏导数定义",
    "target": "偏导数存在",
    "weight": 0.95
  },
  {
    "source": "二元函数连续",
    "target": "偏导数存在与连续的关系",
    "weight": 0.9
  },
  {
    "source": "偏导数存在",
    "target": "偏导数存在与连续的关系",
    "weight": 0.9
  },
  {
    "source": "多元函数偏导数存在",
    "target": "多元函数可微",
    "weight": 0.9
  },
  {
    "source": "多元函数连续",
    "target": "多元函数可微",
    "weight": 0.85
  },
  {
    "source": "多元函数偏导数存在",
    "target": "多元函数连续",
    "weight": 0.1
  },
  {
    "source": "多元函数可微",
    "target": "偏导数存在",
    "weight": 0.85
  },
  {
    "source": "偏导数计算",
    "target": "全微分计算",
    "weight": 0.95
  },
  {
    "source": "基本初等函数求导",
    "target": "复合函数求导法则",
    "weight": 0.8
  },
  {
    "source": "复合函数求导法则",
    "target": "多元函数全微分",
    "weight": 0.9
  },
  {
    "source": "基本初等函数求导",
    "target": "多元函数全微分",
    "weight": 0.75
  },
  {
    "source": "复合函数求导法则",
    "target": "幂指函数求导",
    "weight": 0.85
  },
  {
    "source": "多元函数全微分",
    "target": "幂指函数求导",
    "weight": 0.8
  },
  {
    "source": "一元复合函数求导法则",
    "target": "多元复合函数求导法则",
    "weight": 0.85
  },
  {
    "source": "基本初等函数求导公式",
    "target": "偏导数计算",
    "weight": 0.8
  },
  {
    "source": "幂指函数求导",
    "target": "偏导数计算",
    "weight": 0.85
  },
  {
    "source": "多元复合函数求导法则",
    "target": "偏导数计算",
    "weight": 0.95
  },
  {
    "source": "多元复合函数求导法则",
    "target": "偏导数",
    "weight": 0.85
  },
  {
    "source": "全微分",
    "target": "隐函数的全微分",
    "weight": 0.9
  },
  {
    "source": "隐函数",
    "target": "隐函数的全微分",
    "weight": 0.8
  },
  {
    "source": "一阶微分形式不变性",
    "target": "隐函数的全微分",
    "weight": 0.85
  },
  {
    "source": "极限",
    "target": "偏导数",
    "weight": 0.9
  },
  {
    "source": "偏导数",
    "target": "可微性",
    "weight": 0.95
  },
  {
    "source": "二元函数极限",
    "target": "连续性",
    "weight": 0.9
  },
  {
    "source": "连续性",
    "target": "偏导数存在",
    "weight": 0.7
  },
  {
    "source": "偏导数存在",
    "target": "可微性",
    "weight": 0.9
  },
  {
    "source": "可微性",
    "target": "偏导数连续",
    "weight": 0.85
  },
  {
    "source": "偏导数",
    "target": "全微分定义",
    "weight": 0.9
  },
  {
    "source": "特殊路径法",
    "target": "极限不存在",
    "weight": 0.85
  },
  {
    "source": "极限计算",
    "target": "偏导数定义",
    "weight": 0.9
  },
  {
    "source": "偏导数定义",
    "target": "偏导数存在性",
    "weight": 0.85
  },
  {
    "source": "偏导数存在性",
    "target": "可微性判断",
    "weight": 0.9
  },
  {
    "source": "极限计算",
    "target": "可微性判断",
    "weight": 0.8
  },
  {
    "source": "极限概念",
    "target": "可微性",
    "weight": 0.9
  },
  {
    "source": "偏导数",
    "target": "偏导数连续性",
    "weight": 0.85
  },
  {
    "source": "偏导数连续性",
    "target": "可微性",
    "weight": 0.95
  },
  {
    "source": "链式法则",
    "target": "偏导数计算",
    "weight": 0.9
  },
  {
    "source": "偏导数连续性",
    "target": "复合函数偏导数",
    "weight": 0.8
  },
  {
    "source": "一元函数求导法则",
    "target": "偏导数概念",
    "weight": 0.9
  },
  {
    "source": "一元函数求导法则",
    "target": "多元复合函数求偏导",
    "weight": 0.85
  },
  {
    "source": "多元复合函数求偏导",
    "target": "全导数",
    "weight": 0.95
  },
  {
    "source": "一元函数求导法则",
    "target": "一阶偏导数",
    "weight": 0.9
  },
  {
    "source": "一元函数求导法则",
    "target": "多元复合函数求导法则",
    "weight": 0.85
  },
  {
    "source": "多元复合函数求导法则",
    "target": "二阶偏导数",
    "weight": 0.85
  },
  {
    "source": "偏导数",
    "target": "复合函数求导法则",
    "weight": 0.85
  },
  {
    "source": "偏导数",
    "target": "隐函数求导法则",
    "weight": 0.9
  },
  {
    "source": "一元隐函数求导法则",
    "target": "隐函数求导法则",
    "weight": 0.85
  },
  {
    "source": "连续",
    "target": "隐函数存在定理",
    "weight": 0.85
  },
  {
    "source": "隐函数存在定理（一元）",
    "target": "一元隐函数求导",
    "weight": 0.9
  },
  {
    "source": "偏导数",
    "target": "一元隐函数求导",
    "weight": 0.95
  },
  {
    "source": "隐函数存在定理（二元）",
    "target": "二元隐函数求导",
    "weight": 0.9
  },
  {
    "source": "偏导数",
    "target": "二元隐函数求导",
    "weight": 0.95
  },
  {
    "source": "一元隐函数求导",
    "target": "二元隐函数求导",
    "weight": 0.8
  },
  {
    "source": "极限",
    "target": "方向导数",
    "weight": 0.9
  },
  {
    "source": "邻域",
    "target": "方向导数",
    "weight": 0.7
  },
  {
    "source": "方向导数",
    "target": "梯度",
    "weight": 0.95
  },
  {
    "source": "隐函数存在定理",
    "target": "连续偏导数",
    "weight": 0.8
  },
  {
    "source": "极限概念",
    "target": "方向导数的定义",
    "weight": 0.9
  },
  {
    "source": "方向导数的定义",
    "target": "方向导数的计算",
    "weight": 0.85
  },
  {
    "source": "可微",
    "target": "方向导数的计算",
    "weight": 0.95
  },
  {
    "source": "偏导数",
    "target": "方向导数的计算",
    "weight": 0.9
  },
  {
    "source": "二元函数梯度",
    "target": "三元函数梯度",
    "weight": 0.8
  },
  {
    "source": "向量运算",
    "target": "方向余弦",
    "weight": 0.85
  },
  {
    "source": "法向量",
    "target": "方向余弦",
    "weight": 0.9
  },
  {
    "source": "单位向量",
    "target": "方向余弦",
    "weight": 0.85
  },
  {
    "source": "向径",
    "target": "单位向量",
    "weight": 0.8
  },
  {
    "source": "梯度",
    "target": "散度",
    "weight": 0.85
  },
  {
    "source": "邻域",
    "target": "多元函数极值定义",
    "weight": 0.8
  },
  {
    "source": "多元函数极值定义",
    "target": "极值存在的必要条件",
    "weight": 0.9
  },
  {
    "source": "偏导数",
    "target": "极值存在的必要条件",
    "weight": 0.95
  },
  {
    "source": "可微",
    "target": "极值存在的必要条件",
    "weight": 0.95
  },
  {
    "source": "驻点",
    "target": "二元函数极值充分条件",
    "weight": 0.9
  },
  {
    "source": "二阶偏导数",
    "target": "二元函数极值充分条件",
    "weight": 0.95
  },
  {
    "source": "无条件极值",
    "target": "条件极值",
    "weight": 0.85
  },
  {
    "source": "一阶偏导数",
    "target": "拉格朗日乘数法",
    "weight": 0.9
  },
  {
    "source": "二元函数的连续性",
    "target": "二元函数的最大值和最小值",
    "weight": 0.9
  },
  {
    "source": "极值存在的必要条件",
    "target": "驻点",
    "weight": 0.9
  },
  {
    "source": "驻点",
    "target": "多元函数的极值",
    "weight": 0.85
  },
  {
    "source": "多元函数的极值",
    "target": "二元函数的最大值和最小值",
    "weight": 0.85
  },
  {
    "source": "可微函数极值",
    "target": "驻点",
    "weight": 0.9
  },
  {
    "source": "二元函数极限",
    "target": "函数值计算",
    "weight": 0.85
  },
  {
    "source": "二元函数极限",
    "target": "局部近似",
    "weight": 0.9
  },
  {
    "source": "局部近似",
    "target": "极值判定",
    "weight": 0.9
  },
  {
    "source": "极值点定义",
    "target": "路径法判定极值",
    "weight": 0.85
  },
  {
    "source": "驻点",
    "target": "极值点",
    "weight": 0.85
  },
  {
    "source": "一阶偏导数",
    "target": "隐函数求导",
    "weight": 0.8
  },
  {
    "source": "二阶偏导数",
    "target": "二元函数极值判别式",
    "weight": 0.9
  },
  {
    "source": "二元函数极值判别式",
    "target": "二元函数极值的判定",
    "weight": 0.95
  },
  {
    "source": "隐函数",
    "target": "多元函数极值",
    "weight": 0.8
  },
  {
    "source": "配方法",
    "target": "多元函数极值",
    "weight": 0.7
  },
  {
    "source": "偏导数",
    "target": "多元函数条件极值",
    "weight": 0.9
  },
  {
    "source": "多元函数极值",
    "target": "多元函数条件极值",
    "weight": 0.85
  },
  {
    "source": "拉格朗日乘数法",
    "target": "多元函数条件极值",
    "weight": 0.95
  },
  {
    "source": "全微分",
    "target": "原函数",
    "weight": 0.9
  },
  {
    "source": "偏导数",
    "target": "驻点",
    "weight": 0.95
  },
  {
    "source": "驻点",
    "target": "多元函数最值",
    "weight": 0.9
  },
  {
    "source": "边界极值",
    "target": "多元函数最值",
    "weight": 0.9
  },
  {
    "source": "偏导数",
    "target": "拉格朗日乘数法",
    "weight": 0.9
  },
  {
    "source": "点到直线的距离",
    "target": "条件极值",
    "weight": 0.85
  },
  {
    "source": "椭圆方程",
    "target": "条件极值",
    "weight": 0.85
  },
  {
    "source": "多元函数",
    "target": "条件极值",
    "weight": 0.9
  },
  {
    "source": "多元函数",
    "target": "偏导数",
    "weight": 0.95
  },
  {
    "source": "拉格朗日乘数法",
    "target": "解方程组",
    "weight": 0.85
  },
  {
    "source": "偏导数",
    "target": "条件极值",
    "weight": 0.9
  },
  {
    "source": "椭球面方程",
    "target": "拉格朗日乘数法",
    "weight": 0.8
  },
  {
    "source": "拉格朗日乘数法",
    "target": "多元函数最值",
    "weight": 0.9
  },
  {
    "source": "多元函数极值",
    "target": "多元函数最值",
    "weight": 0.85
  },
  {
    "source": "偏导数",
    "target": "多元函数极值",
    "weight": 0.9
  },
  {
    "source": "偏导数",
    "target": "二元函数泰勒公式",
    "weight": 0.95
  },
  {
    "source": "二元函数泰勒公式",
    "target": "二元函数拉格朗日中值定理",
    "weight": 0.9
  },
  {
    "source": "二元函数泰勒公式",
    "target": "二元函数麦克劳林公式",
    "weight": 0.9
  },
  {
    "source": "偏导数",
    "target": "曲面的切平面与法线",
    "weight": 0.85
  },
  {
    "source": "二重积分的概念",
    "target": "二重积分的性质",
    "weight": 0.85
  },
  {
    "source": "二重积分的概念",
    "target": "直角坐标系下二重积分的计算",
    "weight": 0.95
  },
  {
    "source": "直角坐标系下二重积分的计算",
    "target": "极坐标系下二重积分的计算",
    "weight": 0.85
  },
  {
    "source": "直角坐标系下二重积分的计算",
    "target": "交换积分次序",
    "weight": 0.9
  },
  {
    "source": "三角函数恒等式",
    "target": "定积分计算",
    "weight": 0.8
  },
  {
    "source": "奇偶函数定积分性质",
    "target": "定积分计算",
    "weight": 0.7
  },
  {
    "source": "二重积分",
    "target": "积分区域的对称性",
    "weight": 0.9
  },
  {
    "source": "函数的奇偶性",
    "target": "奇偶函数在对称区域上的积分性质",
    "weight": 0.9
  },
  {
    "source": "积分区域的对称性",
    "target": "奇偶函数在对称区域上的积分性质",
    "weight": 0.95
  },
  {
    "source": "奇偶函数在对称区域上的积分性质",
    "target": "利用对称性计算二重积分",
    "weight": 0.95
  },
  {
    "source": "被积函数的奇偶性",
    "target": "利用对称性计算二重积分",
    "weight": 0.9
  },
  {
    "source": "积分区域的对称性",
    "target": "利用对称性计算二重积分",
    "weight": 0.9
  },
  {
    "source": "积分区域的对称性",
    "target": "二重积分的对称性",
    "weight": 0.9
  },
  {
    "source": "奇偶函数的定义",
    "target": "二重积分的对称性",
    "weight": 0.9
  },
  {
    "source": "直角坐标与球面坐标的关系",
    "target": "球面坐标体积元素",
    "weight": 0.85
  },
  {
    "source": "球面坐标体积元素",
    "target": "三重积分的球面坐标变换",
    "weight": 0.95
  },
  {
    "source": "三重积分的球面坐标变换",
    "target": "三重积分化为累次积分",
    "weight": 0.85
  },
  {
    "source": "三重积分的性质",
    "target": "利用对称性计算三重积分",
    "weight": 0.9
  },
  {
    "source": "空间区域的对称性",
    "target": "三重积分的对称性",
    "weight": 0.9
  },
  {
    "source": "被积函数的奇偶性",
    "target": "三重积分的对称性",
    "weight": 0.9
  },
  {
    "source": "三重积分的对称性",
    "target": "三重积分的计算",
    "weight": 0.85
  },
  {
    "source": "三重积分的概念",
    "target": "三重积分的比较性质",
    "weight": 0.9
  },
  {
    "source": "三重积分的概念",
    "target": "对称性计算三重积分",
    "weight": 0.9
  },
  {
    "source": "积分区域的确定",
    "target": "三重积分的比较性质",
    "weight": 0.8
  },
  {
    "source": "积分区域的确定",
    "target": "对称性计算三重积分",
    "weight": 0.85
  },
  {
    "source": "二重积分的定义与性质",
    "target": "含积分号的函数方程求解",
    "weight": 0.9
  },
  {
    "source": "二重积分的区域可加性",
    "target": "复杂区域二重积分的计算",
    "weight": 0.9
  },
  {
    "source": "二重积分的极坐标变换",
    "target": "极坐标系下二重积分的计算",
    "weight": 0.95
  },
  {
    "source": "奇偶对称性",
    "target": "二重积分的化简计算",
    "weight": 0.85
  },
  {
    "source": "定积分的计算",
    "target": "极坐标系下二重积分的计算",
    "weight": 0.8
  },
  {
    "source": "变限积分求导",
    "target": "函数单调性",
    "weight": 0.85
  },
  {
    "source": "函数连续性",
    "target": "函数单调性",
    "weight": 0.7
  },
  {
    "source": "定积分",
    "target": "柯西积分不等式",
    "weight": 0.8
  },
  {
    "source": "极坐标系下的二重积分",
    "target": "球面坐标系下的三重积分",
    "weight": 0.85
  },
  {
    "source": "定积分",
    "target": "第一类曲线积分",
    "weight": 0.9
  },
  {
    "source": "极限",
    "target": "第一类曲线积分定义（二维）",
    "weight": 0.95
  },
  {
    "source": "连续性",
    "target": "第一类曲线积分存在性",
    "weight": 0.9
  },
  {
    "source": "第一类曲线积分定义（二维）",
    "target": "第一类曲线积分定义（三维）",
    "weight": 0.9
  },
  {
    "source": "第一类曲线积分定义",
    "target": "第一类曲线积分性质",
    "weight": 0.85
  },
  {
    "source": "第一类曲线积分性质",
    "target": "第一类曲线积分计算法",
    "weight": 0.75
  },
  {
    "source": "第一类曲线积分定义",
    "target": "第一类曲线积分计算法",
    "weight": 0.85
  },
  {
    "source": "参数方程求导",
    "target": "弧微分",
    "weight": 0.9
  },
  {
    "source": "弧微分",
    "target": "第一类曲线积分",
    "weight": 0.95
  },
  {
    "source": "导数连续性",
    "target": "第一类曲线积分",
    "weight": 0.7
  },
  {
    "source": "第一类曲线积分",
    "target": "定积分",
    "weight": 0.85
  },
  {
    "source": "直角坐标化参数方程",
    "target": "对坐标的曲线积分计算",
    "weight": 0.9
  },
  {
    "source": "极坐标化参数方程",
    "target": "对坐标的曲线积分计算",
    "weight": 0.9
  },
  {
    "source": "参数方程",
    "target": "对坐标的曲线积分计算",
    "weight": 0.95
  },
  {
    "source": "对坐标的曲线积分的方向性",
    "target": "定积分上下限的确定",
    "weight": 0.9
  },
  {
    "source": "定积分上下限的确定",
    "target": "对坐标的曲线积分计算",
    "weight": 0.9
  },
  {
    "source": "三角函数定积分",
    "target": "对坐标的曲线积分计算",
    "weight": 0.85
  },
  {
    "source": "圆的参数方程",
    "target": "第二类曲线积分计算",
    "weight": 0.8
  },
  {
    "source": "第二类曲线积分的概念",
    "target": "第二类曲线积分的参数化法",
    "weight": 0.85
  },
  {
    "source": "第二类曲线积分的参数化法",
    "target": "第二类曲线积分计算",
    "weight": 0.95
  },
  {
    "source": "定积分的计算",
    "target": "第二类曲线积分计算",
    "weight": 0.9
  },
  {
    "source": "空间直线方程",
    "target": "第二类曲线积分",
    "weight": 0.85
  },
  {
    "source": "定积分",
    "target": "第二类曲线积分",
    "weight": 0.9
  },
  {
    "source": "偏导数",
    "target": "全微分判定条件",
    "weight": 0.9
  },
  {
    "source": "全微分判定条件",
    "target": "全微分",
    "weight": 0.95
  },
  {
    "source": "偏导数计算",
    "target": "全微分判定条件",
    "weight": 0.9
  },
  {
    "source": "全微分判定条件",
    "target": "全微分的定义与计算",
    "weight": 0.9
  },
  {
    "source": "凑微分法",
    "target": "全微分的定义与计算",
    "weight": 0.85
  },
  {
    "source": "极限",
    "target": "第一类曲面积分的定义",
    "weight": 0.8
  },
  {
    "source": "偏导数",
    "target": "曲面面积元素",
    "weight": 0.9
  },
  {
    "source": "曲面面积元素",
    "target": "第一类曲面积分计算",
    "weight": 0.95
  },
  {
    "source": "曲面方程",
    "target": "曲面投影区域",
    "weight": 0.85
  },
  {
    "source": "曲面投影区域",
    "target": "第一类曲面积分计算",
    "weight": 0.9
  },
  {
    "source": "二重积分计算",
    "target": "第一类曲面积分计算",
    "weight": 0.95
  },
  {
    "source": "空间解析几何",
    "target": "曲面投影区域",
    "weight": 0.8
  },
  {
    "source": "偏导数",
    "target": "面积微元",
    "weight": 0.9
  },
  {
    "source": "面积微元",
    "target": "第一类曲面积分计算公式",
    "weight": 0.95
  },
  {
    "source": "第一类曲面积分计算公式",
    "target": "第一类曲面积分",
    "weight": 0.9
  },
  {
    "source": "曲面投影",
    "target": "二重积分",
    "weight": 0.85
  },
  {
    "source": "第一类曲面积分",
    "target": "二重积分",
    "weight": 0.85
  },
  {
    "source": "空间曲面方程",
    "target": "第一型曲面积分",
    "weight": 0.8
  },
  {
    "source": "曲面面积元素计算",
    "target": "第一型曲面积分",
    "weight": 0.9
  },
  {
    "source": "第一型曲面积分",
    "target": "二重积分",
    "weight": 0.95
  },
  {
    "source": "空间曲面方程",
    "target": "空间曲面投影",
    "weight": 0.9
  },
  {
    "source": "偏导数",
    "target": "拉普拉斯算子",
    "weight": 0.9
  },
  {
    "source": "对面积的曲面积分",
    "target": "对坐标的曲面积分",
    "weight": 0.85
  },
  {
    "source": "对坐标的曲面积分",
    "target": "高斯公式",
    "weight": 0.95
  },
  {
    "source": "方向导数",
    "target": "两类曲面积分的关系",
    "weight": 0.9
  },
  {
    "source": "两类曲面积分的关系",
    "target": "高斯公式",
    "weight": 0.85
  },
  {
    "source": "偏导数",
    "target": "乘积求导法则",
    "weight": 0.9
  },
  {
    "source": "二阶偏导数",
    "target": "拉普拉斯算子",
    "weight": 0.95
  },
  {
    "source": "散度",
    "target": "高斯公式",
    "weight": 0.9
  },
  {
    "source": "高斯公式",
    "target": "通量",
    "weight": 0.95
  },
  {
    "source": "第二类曲线积分",
    "target": "第二类曲线积分的性质",
    "weight": 0.9
  },
  {
    "source": "一阶连续偏导数",
    "target": "格林公式",
    "weight": 0.9
  },
  {
    "source": "单连通区域",
    "target": "曲线积分与路径无关",
    "weight": 0.85
  },
  {
    "source": "曲线积分与路径无关",
    "target": "偏导数计算",
    "weight": 0.9
  },
  {
    "source": "偏导数计算",
    "target": "建立微分方程",
    "weight": 0.85
  },
  {
    "source": "建立微分方程",
    "target": "求解微分方程",
    "weight": 0.95
  },
  {
    "source": "求解微分方程",
    "target": "确定任意常数",
    "weight": 0.9
  },
  {
    "source": "偏导数计算",
    "target": "曲线积分与路径无关的条件",
    "weight": 0.9
  },
  {
    "source": "格林公式",
    "target": "曲线积分与路径无关的条件",
    "weight": 0.9
  },
  {
    "source": "曲线积分与路径无关的条件",
    "target": "一阶线性微分方程",
    "weight": 0.85
  },
  {
    "source": "二重积分",
    "target": "格林公式",
    "weight": 0.9
  },
  {
    "source": "拉格朗日乘数法",
    "target": "条件极值",
    "weight": 0.95
  },
  {
    "source": "第二类曲线积分",
    "target": "条件极值",
    "weight": 0.7
  },
  {
    "source": "数列",
    "target": "常数项级数的概念",
    "weight": 0.9
  },
  {
    "source": "常数项级数的概念",
    "target": "常数项级数收敛的概念",
    "weight": 1.0
  },
  {
    "source": "函数项级数的定义",
    "target": "函数项级数的收敛域",
    "weight": 0.9
  },
  {
    "source": "函数项级数的定义",
    "target": "函数项级数的和函数",
    "weight": 0.9
  },
  {
    "source": "函数项级数的收敛域",
    "target": "函数项级数的和函数",
    "weight": 0.85
  },
  {
    "source": "函数项级数的定义",
    "target": "幂级数的定义",
    "weight": 0.95
  },
  {
    "source": "函数项级数的收敛域",
    "target": "幂级数的收敛域",
    "weight": 0.95
  },
  {
    "source": "幂级数",
    "target": "阿贝尔引理",
    "weight": 0.9
  },
  {
    "source": "绝对收敛",
    "target": "阿贝尔引理",
    "weight": 0.85
  },
  {
    "source": "阿贝尔引理",
    "target": "收敛半径",
    "weight": 0.95
  },
  {
    "source": "收敛半径",
    "target": "收敛域",
    "weight": 0.95
  },
  {
    "source": "函数项级数",
    "target": "幂级数",
    "weight": 0.8
  },
  {
    "source": "比值判别法",
    "target": "绝对收敛",
    "weight": 0.9
  },
  {
    "source": "级数收敛的必要条件",
    "target": "收敛域",
    "weight": 0.8
  },
  {
    "source": "绝对收敛",
    "target": "收敛域",
    "weight": 0.85
  },
  {
    "source": "阿贝尔引理",
    "target": "幂级数收敛性",
    "weight": 0.95
  },
  {
    "source": "莱布尼兹定理",
    "target": "交错级数敛散性",
    "weight": 0.9
  },
  {
    "source": "阿贝尔引理",
    "target": "幂级数敛散性",
    "weight": 0.9
  },
  {
    "source": "比值审敛法",
    "target": "收敛半径",
    "weight": 0.95
  },
  {
    "source": "莱布尼茨判别法",
    "target": "收敛域",
    "weight": 0.8
  },
  {
    "source": "调和级数",
    "target": "收敛域",
    "weight": 0.75
  },
  {
    "source": "比值审敛法",
    "target": "幂级数收敛半径",
    "weight": 0.9
  },
  {
    "source": "变量代换法",
    "target": "幂级数收敛半径",
    "weight": 0.85
  },
  {
    "source": "极限",
    "target": "比值审敛法",
    "weight": 0.85
  },
  {
    "source": "比值审敛法",
    "target": "幂级数收敛域",
    "weight": 0.95
  },
  {
    "source": "幂级数",
    "target": "幂级数收敛域",
    "weight": 0.9
  },
  {
    "source": "常用泰勒展开式",
    "target": "幂级数和函数",
    "weight": 0.85
  },
  {
    "source": "导数运算",
    "target": "指数函数求导",
    "weight": 0.9
  },
  {
    "source": "导数运算",
    "target": "函数求导法则",
    "weight": 0.9
  },
  {
    "source": "等比级数求和公式",
    "target": "幂级数逐项积分",
    "weight": 0.8
  },
  {
    "source": "幂级数逐项积分",
    "target": "幂级数求和函数",
    "weight": 0.95
  },
  {
    "source": "函数求导法则",
    "target": "幂级数求和函数",
    "weight": 0.85
  },
  {
    "source": "幂级数求和函数",
    "target": "构造幂级数法",
    "weight": 0.9
  },
  {
    "source": "构造幂级数法",
    "target": "数项级数求和",
    "weight": 0.95
  },
  {
    "source": "等比级数求和",
    "target": "幂级数求和",
    "weight": 0.85
  },
  {
    "source": "幂级数",
    "target": "和函数",
    "weight": 0.95
  },
  {
    "source": "幂级数求和",
    "target": "和函数",
    "weight": 0.95
  },
  {
    "source": "和函数",
    "target": "数项级数求和",
    "weight": 0.9
  },
  {
    "source": "几何级数求和公式",
    "target": "幂级数逐项求导",
    "weight": 0.85
  },
  {
    "source": "幂级数收敛半径",
    "target": "幂级数求和函数",
    "weight": 0.9
  },
  {
    "source": "幂级数求和函数",
    "target": "数项级数求和",
    "weight": 0.9
  },
  {
    "source": "任意阶导数",
    "target": "泰勒级数",
    "weight": 0.9
  },
  {
    "source": "泰勒级数",
    "target": "麦克劳林级数",
    "weight": 0.95
  },
  {
    "source": "泰勒级数",
    "target": "函数展开成幂级数",
    "weight": 0.85
  },
  {
    "source": "麦克劳林级数",
    "target": "函数展开成幂级数",
    "weight": 0.8
  },
  {
    "source": "函数展开成幂级数",
    "target": "幂级数展开的直接方法",
    "weight": 0.8
  },
  {
    "source": "函数展开成幂级数",
    "target": "幂级数展开的间接方法",
    "weight": 0.8
  },
  {
    "source": "级数与积分的交换",
    "target": "幂级数求和",
    "weight": 0.8
  },
  {
    "source": "定积分计算",
    "target": "级数与积分的交换",
    "weight": 0.7
  },
  {
    "source": "对数函数性质",
    "target": "幂级数求和",
    "weight": 0.6
  },
  {
    "source": "连续",
    "target": "一元函数微分学",
    "weight": 0.85
  },
  {
    "source": "一元函数微分学",
    "target": "一元函数积分学",
    "weight": 0.95
  },
  {
    "source": "一元函数微分学",
    "target": "微分方程",
    "weight": 0.85
  },
  {
    "source": "一元函数积分学",
    "target": "微分方程",
    "weight": 0.85
  },
  {
    "source": "一元函数微分学",
    "target": "多元函数微分学",
    "weight": 0.9
  },
  {
    "source": "空间解析几何与向量代数",
    "target": "多元函数积分学",
    "weight": 0.8
  },
  {
    "source": "多元函数微分学",
    "target": "多元函数积分学",
    "weight": 0.85
  },
  {
    "source": "一元函数积分学",
    "target": "多元函数积分学",
    "weight": 0.8
  },
  {
    "source": "一元函数积分学",
    "target": "无穷级数",
    "weight": 0.7
  },
  {
    "source": "映射",
    "target": "函数",
    "weight": 0.9
  },
  {
    "source": "极限",
    "target": "一元函数微分学",
    "weight": 0.9
  },
  {
    "source": "函数",
    "target": "自然定义域",
    "weight": 0.8
  },
  {
    "source": "偶次根式性质",
    "target": "复合函数定义域",
    "weight": 0.9
  },
  {
    "source": "分式性质",
    "target": "复合函数定义域",
    "weight": 0.9
  },
  {
    "source": "对数函数定义域",
    "target": "复合函数定义域",
    "weight": 0.9
  },
  {
    "source": "反三角函数定义域",
    "target": "复合函数定义域",
    "weight": 0.9
  },
  {
    "source": "一元二次不等式解法",
    "target": "复合函数定义域",
    "weight": 0.85
  },
  {
    "source": "绝对值不等式解法",
    "target": "复合函数定义域",
    "weight": 0.85
  },
  {
    "source": "简单函数的定义域",
    "target": "函数自然定义域",
    "weight": 0.9
  },
  {
    "source": "集合的交集运算",
    "target": "函数自然定义域",
    "weight": 0.85
  },
  {
    "source": "分母不为零",
    "target": "分式函数的定义域",
    "weight": 0.95
  },
  {
    "source": "被开方数非负",
    "target": "偶次根式的定义域",
    "weight": 0.95
  },
  {
    "source": "对数真数大于零",
    "target": "对数函数的定义域",
    "weight": 0.95
  },
  {
    "source": "分式函数的定义域",
    "target": "简单函数的定义域",
    "weight": 0.8
  },
  {
    "source": "偶次根式的定义域",
    "target": "简单函数的定义域",
    "weight": 0.8
  },
  {
    "source": "对数函数的定义域",
    "target": "简单函数的定义域",
    "weight": 0.8
  },
  {
    "source": "函数的定义域",
    "target": "函数相同的判定条件",
    "weight": 0.9
  },
  {
    "source": "函数的对应法则",
    "target": "函数相同的判定条件",
    "weight": 0.9
  },
  {
    "source": "三角函数的定义域",
    "target": "函数的定义域",
    "weight": 0.8
  },
  {
    "source": "反三角函数的定义域",
    "target": "函数的定义域",
    "weight": 0.8
  },
  {
    "source": "函数相同的判定条件",
    "target": "判断两函数是否相同",
    "weight": 0.9
  },
  {
    "source": "三角函数求值",
    "target": "函数作图",
    "weight": 0.8
  },
  {
    "source": "绝对值",
    "target": "函数作图",
    "weight": 0.7
  },
  {
    "source": "函数奇偶性",
    "target": "函数单调性",
    "weight": 0.9
  },
  {
    "source": "函数奇偶性",
    "target": "函数作图",
    "weight": 0.8
  },
  {
    "source": "函数单调性",
    "target": "函数作图",
    "weight": 0.7
  },
  {
    "source": "奇函数的定义",
    "target": "奇函数的单调性对称性",
    "weight": 0.9
  },
  {
    "source": "函数单调性的定义",
    "target": "奇函数的单调性对称性",
    "weight": 0.85
  },
  {
    "source": "偶函数的定义",
    "target": "奇偶函数的运算性质",
    "weight": 0.9
  },
  {
    "source": "奇函数的定义",
    "target": "奇偶函数的运算性质",
    "weight": 0.9
  },
  {
    "source": "偶函数的定义",
    "target": "偶函数的乘积性质",
    "weight": 0.9
  },
  {
    "source": "奇函数的定义",
    "target": "奇函数的乘积性质",
    "weight": 0.9
  },
  {
    "source": "偶函数的定义",
    "target": "奇偶函数的乘积性质",
    "weight": 0.9
  },
  {
    "source": "奇函数的定义",
    "target": "奇偶函数的乘积性质",
    "weight": 0.9
  },
  {
    "source": "偶函数的乘积性质",
    "target": "函数奇偶性的判断",
    "weight": 0.8
  },
  {
    "source": "奇函数的乘积性质",
    "target": "函数奇偶性的判断",
    "weight": 0.8
  },
  {
    "source": "奇偶函数的乘积性质",
    "target": "函数奇偶性的判断",
    "weight": 0.8
  },
  {
    "source": "函数求值(计算f(-x))",
    "target": "偶函数定义(f(-x)=f(x))",
    "weight": 0.85
  },
  {
    "source": "函数求值(计算f(-x))",
    "target": "奇函数定义(f(-x)=-f(x))",
    "weight": 0.85
  },
  {
    "source": "偶函数定义(f(-x)=f(x))",
    "target": "函数奇偶性判定",
    "weight": 0.9
  },
  {
    "source": "奇函数定义(f(-x)=-f(x))",
    "target": "函数奇偶性判定",
    "weight": 0.9
  },
  {
    "source": "函数奇偶性定义",
    "target": "函数奇偶性判断",
    "weight": 0.9
  },
  {
    "source": "周期函数定义",
    "target": "周期函数判断",
    "weight": 0.9
  },
  {
    "source": "三角函数周期性",
    "target": "周期函数判断",
    "weight": 0.85
  },
  {
    "source": "反函数定义",
    "target": "反函数求解",
    "weight": 0.9
  },
  {
    "source": "单射",
    "target": "反函数存在条件",
    "weight": 0.95
  },
  {
    "source": "单调性",
    "target": "单射",
    "weight": 0.9
  },
  {
    "source": "反函数概念",
    "target": "反函数求解",
    "weight": 0.9
  },
  {
    "source": "正弦函数",
    "target": "反正弦函数",
    "weight": 0.85
  },
  {
    "source": "指数函数",
    "target": "反函数",
    "weight": 0.85
  },
  {
    "source": "对数函数",
    "target": "反函数",
    "weight": 0.85
  },
  {
    "source": "函数上界",
    "target": "函数有界性",
    "weight": 0.9
  },
  {
    "source": "函数下界",
    "target": "函数有界性",
    "weight": 0.9
  },
  {
    "source": "函数有界性",
    "target": "充分必要条件",
    "weight": 0.75
  },
  {
    "source": "函数的概念",
    "target": "复合函数的概念",
    "weight": 0.9
  },
  {
    "source": "复合函数的概念",
    "target": "复合函数求值",
    "weight": 0.85
  },
  {
    "source": "函数的定义域",
    "target": "复合函数的定义域",
    "weight": 0.9
  },
  {
    "source": "复合函数的概念",
    "target": "复合函数的定义域",
    "weight": 0.9
  },
  {
    "source": "复合函数的定义域",
    "target": "抽象函数的定义域",
    "weight": 0.9
  },
  {
    "source": "函数定义域",
    "target": "复合函数定义域",
    "weight": 0.9
  },
  {
    "source": "不等式求解",
    "target": "复合函数定义域",
    "weight": 0.85
  },
  {
    "source": "复合函数",
    "target": "分段复合函数",
    "weight": 0.9
  },
  {
    "source": "分段函数",
    "target": "分段复合函数",
    "weight": 0.85
  },
  {
    "source": "指数函数",
    "target": "分段复合函数",
    "weight": 0.75
  },
  {
    "source": "分段函数",
    "target": "复合函数",
    "weight": 0.85
  },
  {
    "source": "指数函数",
    "target": "复合函数",
    "weight": 0.8
  },
  {
    "source": "三角函数",
    "target": "建立函数关系式",
    "weight": 0.9
  },
  {
    "source": "梯形面积公式",
    "target": "建立函数关系式",
    "weight": 0.85
  },
  {
    "source": "建立函数关系式",
    "target": "求函数定义域",
    "weight": 0.95
  },
  {
    "source": "解不等式",
    "target": "求函数定义域",
    "weight": 0.9
  },
  {
    "source": "直线方程",
    "target": "面积计算",
    "weight": 0.9
  },
  {
    "source": "面积计算",
    "target": "分段函数",
    "weight": 0.9
  },
  {
    "source": "直线方程",
    "target": "分段函数",
    "weight": 0.8
  },
  {
    "source": "待定系数法",
    "target": "一次函数",
    "weight": 0.85
  },
  {
    "source": "一次函数",
    "target": "一元一次方程",
    "weight": 0.85
  },
  {
    "source": "勾股定理",
    "target": "不等式",
    "weight": 0.8
  },
  {
    "source": "勾股定理",
    "target": "分段函数",
    "weight": 0.9
  },
  {
    "source": "不等式",
    "target": "分段函数",
    "weight": 0.85
  },
  {
    "source": "函数定义域",
    "target": "分段函数",
    "weight": 0.95
  },
  {
    "source": "相似三角形性质",
    "target": "三角形面积公式",
    "weight": 0.9
  },
  {
    "source": "直角三角形性质",
    "target": "三角形面积公式",
    "weight": 0.85
  },
  {
    "source": "三角形面积公式",
    "target": "分段函数",
    "weight": 0.9
  },
  {
    "source": "数列的概念",
    "target": "数列的收敛与发散",
    "weight": 0.9
  },
  {
    "source": "数列的收敛与发散",
    "target": "数列极限",
    "weight": 0.95
  },
  {
    "source": "指数函数",
    "target": "指数模型",
    "weight": 0.85
  },
  {
    "source": "初等函数",
    "target": "分段函数",
    "weight": 0.8
  },
  {
    "source": "数列极限",
    "target": "数列收敛",
    "weight": 0.95
  },
  {
    "source": "数列极限",
    "target": "数列发散",
    "weight": 0.95
  },
  {
    "source": "数列有界性",
    "target": "数列收敛",
    "weight": 0.9
  },
  {
    "source": "数列无界",
    "target": "数列发散",
    "weight": 0.9
  },
  {
    "source": "数列极限概念",
    "target": "数列极限计算",
    "weight": 0.85
  },
  {
    "source": "绝对值与距离",
    "target": "数列极限的ε-N定义",
    "weight": 0.9
  },
  {
    "source": "任意正数与无穷小",
    "target": "数列极限的ε-N定义",
    "weight": 0.85
  },
  {
    "source": "数列极限的ε-N定义",
    "target": "极限等价定义辨析",
    "weight": 0.9
  },
  {
    "source": "数列极限的ε-N定义",
    "target": "子列的极限",
    "weight": 0.9
  },
  {
    "source": "数列极限的ε-N定义",
    "target": "数列极限的存在性",
    "weight": 0.85
  },
  {
    "source": "子列的极限",
    "target": "数列极限的存在性",
    "weight": 0.95
  },
  {
    "source": "左极限",
    "target": "极限存在的充要条件",
    "weight": 0.9
  },
  {
    "source": "右极限",
    "target": "极限存在的充要条件",
    "weight": 0.9
  },
  {
    "source": "极限存在的充要条件",
    "target": "函数极限",
    "weight": 0.85
  },
  {
    "source": "函数极限",
    "target": "极限与函数值的关系",
    "weight": 0.8
  },
  {
    "source": "数列极限的ε-N定义",
    "target": "数列极限",
    "weight": 0.9
  },
  {
    "source": "绝对值函数",
    "target": "左极限",
    "weight": 0.7
  },
  {
    "source": "绝对值函数",
    "target": "右极限",
    "weight": 0.7
  },
  {
    "source": "函数极限的定义",
    "target": "使用定义证明极限",
    "weight": 0.95
  },
  {
    "source": "绝对值不等式",
    "target": "使用定义证明极限",
    "weight": 0.85
  },
  {
    "source": "函数极限的定义",
    "target": "多项式函数的极限",
    "weight": 0.8
  },
  {
    "source": "多项式函数的极限",
    "target": "有理函数的极限",
    "weight": 0.85
  },
  {
    "source": "极限的ε-δ定义",
    "target": "多项式极限",
    "weight": 0.9
  },
  {
    "source": "绝对值不等式",
    "target": "多项式极限",
    "weight": 0.85
  },
  {
    "source": "极限的ε-δ定义",
    "target": "0/0型分式极限",
    "weight": 0.9
  },
  {
    "source": "绝对值不等式",
    "target": "0/0型分式极限",
    "weight": 0.85
  },
  {
    "source": "因式分解",
    "target": "0/0型分式极限",
    "weight": 0.95
  },
  {
    "source": "多项式极限",
    "target": "0/0型分式极限",
    "weight": 0.8
  },
  {
    "source": "极限的ε-δ定义",
    "target": "极限证明",
    "weight": 1.0
  },
  {
    "source": "绝对值不等式",
    "target": "极限证明",
    "weight": 0.9
  },
  {
    "source": "代数化简",
    "target": "极限证明",
    "weight": 0.8
  },
  {
    "source": "极限的ε-δ定义",
    "target": "极限计算",
    "weight": 0.7
  },
  {
    "source": "极限的ε-X定义",
    "target": "极限的证明",
    "weight": 0.95
  },
  {
    "source": "绝对值不等式求解",
    "target": "极限的证明",
    "weight": 0.85
  },
  {
    "source": "极限的ε-X定义",
    "target": "绝对值不等式求解",
    "weight": 0.8
  },
  {
    "source": "放缩法",
    "target": "极限的ε-X定义",
    "weight": 0.9
  },
  {
    "source": "放缩法",
    "target": "极限的ε-δ定义",
    "weight": 0.9
  },
  {
    "source": "局部有界性",
    "target": "极限的ε-δ定义",
    "weight": 0.85
  },
  {
    "source": "极限的ε-X定义",
    "target": "函数极限(趋于无穷)",
    "weight": 1.0
  },
  {
    "source": "极限的ε-δ定义",
    "target": "函数极限(趋于有限值)",
    "weight": 1.0
  },
  {
    "source": "极限的定义(ε-δ语言)",
    "target": "极限证明中的求δ(或X)方法",
    "weight": 0.9
  },
  {
    "source": "极限的定义(ε-X语言)",
    "target": "极限证明中的求δ(或X)方法",
    "weight": 0.9
  },
  {
    "source": "不等式放缩法",
    "target": "极限证明中的求δ(或X)方法",
    "weight": 0.85
  },
  {
    "source": "极限的概念",
    "target": "无穷小量",
    "weight": 0.9
  },
  {
    "source": "不等式放缩法",
    "target": "无穷小量",
    "weight": 0.75
  },
  {
    "source": "极限的定义",
    "target": "无穷小",
    "weight": 0.9
  },
  {
    "source": "极限的定义",
    "target": "无穷大",
    "weight": 0.9
  },
  {
    "source": "绝对值三角不等式",
    "target": "无穷大",
    "weight": 0.8
  },
  {
    "source": "极限定义",
    "target": "无穷小",
    "weight": 0.9
  },
  {
    "source": "极限定义",
    "target": "无穷大",
    "weight": 0.9
  },
  {
    "source": "无穷小",
    "target": "极限四则运算",
    "weight": 0.8
  },
  {
    "source": "极限四则运算",
    "target": "极限计算",
    "weight": 0.85
  },
  {
    "source": "无穷大定义",
    "target": "放缩法证明无穷大",
    "weight": 0.85
  },
  {
    "source": "极限",
    "target": "无穷大",
    "weight": 0.9
  },
  {
    "source": "极限",
    "target": "无穷小",
    "weight": 0.9
  },
  {
    "source": "无穷大",
    "target": "无界",
    "weight": 0.85
  },
  {
    "source": "极限",
    "target": "水平渐近线",
    "weight": 0.9
  },
  {
    "source": "水平渐近线",
    "target": "渐近线",
    "weight": 0.8
  },
  {
    "source": "无穷极限",
    "target": "铅直渐近线",
    "weight": 0.9
  },
  {
    "source": "极限的运算法则",
    "target": "0/0型未定式极限",
    "weight": 0.85
  },
  {
    "source": "极限的运算法则",
    "target": "∞/∞型未定式极限",
    "weight": 0.85
  },
  {
    "source": "等比数列求和",
    "target": "数列极限",
    "weight": 0.75
  },
  {
    "source": "等差数列求和",
    "target": "数列极限",
    "weight": 0.75
  },
  {
    "source": "极限基本概念",
    "target": "0/0型未定式极限",
    "weight": 0.9
  },
  {
    "source": "因式分解",
    "target": "0/0型未定式极限",
    "weight": 0.85
  },
  {
    "source": "0/0型未定式极限",
    "target": "约分化简求极限",
    "weight": 0.9
  },
  {
    "source": "极限基本概念",
    "target": "直接代入法求极限",
    "weight": 0.9
  },
  {
    "source": "极限基本概念",
    "target": "无穷大比无穷大数列极限",
    "weight": 0.85
  },
  {
    "source": "无穷大比无穷大数列极限",
    "target": "分子分母同除最高次幂",
    "weight": 0.9
  },
  {
    "source": "因式分解",
    "target": "分式嵌套极限",
    "weight": 0.8
  },
  {
    "source": "极限的四则运算",
    "target": "代数化简求极限",
    "weight": 0.8
  },
  {
    "source": "极限的四则运算",
    "target": "有理函数在无穷远处的极限",
    "weight": 0.85
  },
  {
    "source": "无穷大分之1的极限",
    "target": "有理函数在无穷远处的极限",
    "weight": 0.9
  },
  {
    "source": "因式分解",
    "target": "0/0型未定式",
    "weight": 0.9
  },
  {
    "source": "0/0型未定式",
    "target": "连续函数代入法",
    "weight": 0.85
  },
  {
    "source": "极限的四则运算法则",
    "target": "无穷大极限计算",
    "weight": 0.8
  },
  {
    "source": "等比数列求和公式",
    "target": "数列极限",
    "weight": 0.9
  },
  {
    "source": "函数极限概念",
    "target": "极限的四则运算法则",
    "weight": 0.85
  },
  {
    "source": "无穷小",
    "target": "无穷小与无穷大的关系",
    "weight": 0.9
  },
  {
    "source": "无穷大",
    "target": "无穷小与无穷大的关系",
    "weight": 0.9
  },
  {
    "source": "有界函数",
    "target": "无穷小乘有界变量",
    "weight": 0.85
  },
  {
    "source": "无穷小",
    "target": "无穷小乘有界变量",
    "weight": 0.85
  },
  {
    "source": "极限的运算",
    "target": "无穷小与无穷大的关系",
    "weight": 0.7
  },
  {
    "source": "极限的运算",
    "target": "无穷小乘有界变量",
    "weight": 0.7
  },
  {
    "source": "无穷小量",
    "target": "无穷小量乘有界函数",
    "weight": 0.9
  },
  {
    "source": "有界函数",
    "target": "无穷小量乘有界函数",
    "weight": 0.9
  },
  {
    "source": "数列极限",
    "target": "极限保号性",
    "weight": 0.95
  },
  {
    "source": "数列极限",
    "target": "极限运算法则",
    "weight": 0.9
  },
  {
    "source": "无穷大量",
    "target": "极限运算法则",
    "weight": 0.85
  },
  {
    "source": "极限的四则运算法则",
    "target": "极限的存在性",
    "weight": 0.85
  },
  {
    "source": "极限的存在性",
    "target": "反证法证明极限问题",
    "weight": 0.8
  },
  {
    "source": "极限的概念",
    "target": "夹逼准则",
    "weight": 0.85
  },
  {
    "source": "夹逼准则",
    "target": "第一个重要极限",
    "weight": 0.95
  },
  {
    "source": "极限的四则运算法则",
    "target": "第一个重要极限",
    "weight": 0.8
  },
  {
    "source": "极限的概念",
    "target": "极限不存在的反例构造",
    "weight": 0.7
  },
  {
    "source": "极限的概念",
    "target": "第一个重要极限",
    "weight": 0.9
  },
  {
    "source": "极限运算法则",
    "target": "第一个重要极限应用",
    "weight": 0.85
  },
  {
    "source": "第一个重要极限",
    "target": "等价无穷小替换",
    "weight": 0.9
  },
  {
    "source": "三角函数公式",
    "target": "含三角函数的极限计算",
    "weight": 0.8
  },
  {
    "source": "第一个重要极限",
    "target": "含三角函数的极限计算",
    "weight": 0.9
  },
  {
    "source": "等价无穷小替换",
    "target": "含三角函数的极限计算",
    "weight": 0.85
  },
  {
    "source": "第一个重要极限",
    "target": "三角函数极限求解",
    "weight": 0.95
  },
  {
    "source": "极限的四则运算法则",
    "target": "极限求解",
    "weight": 0.85
  },
  {
    "source": "三角函数恒等变换",
    "target": "三角函数极限求解",
    "weight": 0.8
  },
  {
    "source": "二倍角公式",
    "target": "三角函数极限求解",
    "weight": 0.8
  },
  {
    "source": "第二个重要极限",
    "target": "1的无穷次方型极限求解",
    "weight": 0.95
  },
  {
    "source": "极限的定义",
    "target": "夹逼准则",
    "weight": 0.85
  },
  {
    "source": "极限的定义",
    "target": "第二重要极限",
    "weight": 0.9
  },
  {
    "source": "极限的定义",
    "target": "极限的计算",
    "weight": 0.85
  },
  {
    "source": "第二重要极限",
    "target": "极限的计算",
    "weight": 0.9
  },
  {
    "source": "夹逼准则",
    "target": "极限的计算",
    "weight": 0.8
  },
  {
    "source": "极限概念",
    "target": "第二重要极限",
    "weight": 0.9
  },
  {
    "source": "极限概念",
    "target": "夹逼准则",
    "weight": 0.95
  },
  {
    "source": "数列有界性",
    "target": "数列单调性",
    "weight": 0.7
  },
  {
    "source": "数列单调性",
    "target": "单调有界准则",
    "weight": 0.9
  },
  {
    "source": "单调有界准则",
    "target": "递推数列求极限",
    "weight": 0.95
  },
  {
    "source": "单调有界定理",
    "target": "数列极限存在",
    "weight": 0.95
  },
  {
    "source": "数列极限存在",
    "target": "递推数列求极限",
    "weight": 0.95
  },
  {
    "source": "夹逼准则",
    "target": "函数极限求解",
    "weight": 0.9
  },
  {
    "source": "无穷小概念",
    "target": "高阶无穷小",
    "weight": 0.9
  },
  {
    "source": "极限计算",
    "target": "无穷小的比较",
    "weight": 0.95
  },
  {
    "source": "因式分解",
    "target": "极限计算",
    "weight": 0.85
  },
  {
    "source": "无穷小的比较",
    "target": "高阶无穷小",
    "weight": 0.9
  },
  {
    "source": "无穷小的比较",
    "target": "同阶无穷小",
    "weight": 0.9
  },
  {
    "source": "无穷小的比较",
    "target": "等价无穷小",
    "weight": 0.9
  },
  {
    "source": "等价无穷小",
    "target": "常见等价无穷小公式",
    "weight": 0.9
  },
  {
    "source": "无穷小量",
    "target": "等价无穷小代换",
    "weight": 0.9
  },
  {
    "source": "等价无穷小代换",
    "target": "常用等价无穷小公式",
    "weight": 0.85
  },
  {
    "source": "极限计算方法",
    "target": "等价无穷小代换",
    "weight": 0.95
  },
  {
    "source": "等价无穷小代换",
    "target": "加减法等价无穷小代换原则",
    "weight": 0.9
  },
  {
    "source": "等价无穷小",
    "target": "等价无穷小代换",
    "weight": 0.95
  },
  {
    "source": "等价无穷小代换",
    "target": "等价无穷小代换加减项限制",
    "weight": 0.85
  },
  {
    "source": "等价无穷小",
    "target": "等价关系性质",
    "weight": 0.8
  },
  {
    "source": "等价无穷小的定义",
    "target": "等价无穷小的传递性",
    "weight": 0.9
  },
  {
    "source": "极限的乘法运算法则",
    "target": "等价无穷小的传递性",
    "weight": 0.85
  },
  {
    "source": "函数连续性",
    "target": "间断点",
    "weight": 0.9
  },
  {
    "source": "间断点",
    "target": "可去间断点",
    "weight": 0.9
  },
  {
    "source": "可去间断点",
    "target": "补充或修改定义使函数连续",
    "weight": 0.8
  },
  {
    "source": "左极限与右极限",
    "target": "连续性",
    "weight": 0.95
  },
  {
    "source": "连续性",
    "target": "右连续",
    "weight": 0.85
  },
  {
    "source": "极限的计算",
    "target": "间断点的判断",
    "weight": 0.9
  },
  {
    "source": "连续性",
    "target": "间断点的分类",
    "weight": 0.85
  },
  {
    "source": "第一类间断点",
    "target": "可去间断点",
    "weight": 0.9
  },
  {
    "source": "第二类间断点",
    "target": "无穷间断点",
    "weight": 0.9
  },
  {
    "source": "等价无穷小",
    "target": "极限的计算",
    "weight": 0.85
  },
  {
    "source": "函数的定义域",
    "target": "间断点的判断",
    "weight": 0.8
  },
  {
    "source": "代数式化简",
    "target": "极限的计算",
    "weight": 0.8
  },
  {
    "source": "极限计算",
    "target": "连续性",
    "weight": 0.9
  },
  {
    "source": "极限计算",
    "target": "间断点分类",
    "weight": 0.85
  },
  {
    "source": "可去间断点",
    "target": "连续延拓",
    "weight": 0.85
  },
  {
    "source": "极限",
    "target": "间断点",
    "weight": 0.9
  },
  {
    "source": "极限不存在",
    "target": "第二类间断点",
    "weight": 0.95
  },
  {
    "source": "左右极限",
    "target": "第一类间断点",
    "weight": 0.9
  },
  {
    "source": "左右极限",
    "target": "跳跃间断点",
    "weight": 0.95
  },
  {
    "source": "间断点",
    "target": "分段函数连续性",
    "weight": 0.85
  },
  {
    "source": "左极限",
    "target": "第一类间断点",
    "weight": 0.9
  },
  {
    "source": "右极限",
    "target": "第一类间断点",
    "weight": 0.9
  },
  {
    "source": "第一类间断点",
    "target": "跳跃间断点",
    "weight": 0.85
  },
  {
    "source": "函数连续性",
    "target": "绝对值函数连续性",
    "weight": 0.9
  },
  {
    "source": "绝对值不等式",
    "target": "绝对值函数连续性",
    "weight": 0.8
  },
  {
    "source": "极限定义",
    "target": "连续性",
    "weight": 0.95
  },
  {
    "source": "邻域",
    "target": "连续性定义",
    "weight": 0.85
  },
  {
    "source": "连续性",
    "target": "局部保号性",
    "weight": 0.9
  },
  {
    "source": "分段函数",
    "target": "间断点",
    "weight": 0.8
  },
  {
    "source": "函数极限的ε-δ定义",
    "target": "函数连续性",
    "weight": 0.9
  },
  {
    "source": "数列极限",
    "target": "海涅定理",
    "weight": 0.9
  },
  {
    "source": "海涅定理",
    "target": "函数极限存在性",
    "weight": 0.85
  },
  {
    "source": "函数极限存在性",
    "target": "函数连续性",
    "weight": 0.95
  },
  {
    "source": "间断点",
    "target": "无穷间断点",
    "weight": 0.95
  },
  {
    "source": "三角函数性质",
    "target": "无穷间断点",
    "weight": 0.75
  },
  {
    "source": "连续函数的运算",
    "target": "初等函数的连续性",
    "weight": 0.85
  },
  {
    "source": "初等函数的连续性",
    "target": "连续区间",
    "weight": 0.9
  },
  {
    "source": "函数定义域",
    "target": "间断点",
    "weight": 0.8
  },
  {
    "source": "因式分解与约分",
    "target": "有理函数的极限",
    "weight": 0.9
  },
  {
    "source": "函数的连续性",
    "target": "连续函数的运算性质",
    "weight": 0.9
  },
  {
    "source": "连续函数的运算性质",
    "target": "最大值与最小值函数的连续性",
    "weight": 0.95
  },
  {
    "source": "函数的连续性",
    "target": "复合函数求极限",
    "weight": 0.85
  },
  {
    "source": "极限的概念",
    "target": "函数的连续性",
    "weight": 0.95
  },
  {
    "source": "极限的概念",
    "target": "导数定义",
    "weight": 0.9
  },
  {
    "source": "极限的概念",
    "target": "有理化方法",
    "weight": 0.8
  },
  {
    "source": "导数定义",
    "target": "洛必达法则",
    "weight": 0.9
  },
  {
    "source": "分子有理化",
    "target": "无理式极限计算",
    "weight": 0.95
  },
  {
    "source": "和差化积公式",
    "target": "三角函数极限计算",
    "weight": 0.85
  },
  {
    "source": "第一重要极限",
    "target": "三角函数极限计算",
    "weight": 0.95
  },
  {
    "source": "极限的四则运算法则",
    "target": "极限的计算",
    "weight": 0.9
  },
  {
    "source": "极限的概念",
    "target": "连续函数的极限",
    "weight": 0.9
  },
  {
    "source": "极限的概念",
    "target": "重要极限一",
    "weight": 0.9
  },
  {
    "source": "极限的概念",
    "target": "重要极限二",
    "weight": 0.9
  },
  {
    "source": "函数的连续性",
    "target": "函数的间断点",
    "weight": 0.95
  },
  {
    "source": "函数的连续性",
    "target": "复合函数的连续性",
    "weight": 0.9
  },
  {
    "source": "连续函数的极限",
    "target": "复合函数的连续性",
    "weight": 0.85
  },
  {
    "source": "连续性",
    "target": "连续函数的运算性质",
    "weight": 0.85
  },
  {
    "source": "连续函数的运算性质",
    "target": "间断点判断",
    "weight": 0.8
  },
  {
    "source": "连续性",
    "target": "分段函数的连续性",
    "weight": 0.85
  },
  {
    "source": "初等函数的连续性",
    "target": "连续性",
    "weight": 0.9
  },
  {
    "source": "连续性",
    "target": "闭区间上连续函数的性质",
    "weight": 0.9
  },
  {
    "source": "零点定理",
    "target": "不动点",
    "weight": 0.8
  },
  {
    "source": "零点定理",
    "target": "方程的根",
    "weight": 0.9
  },
  {
    "source": "零点定理",
    "target": "方程根的存在性",
    "weight": 0.85
  },
  {
    "source": "连续函数",
    "target": "零点定理",
    "weight": 0.9
  },
  {
    "source": "零点定理",
    "target": "方程实根的存在性",
    "weight": 0.85
  },
  {
    "source": "充分条件",
    "target": "充分必要条件",
    "weight": 0.7
  },
  {
    "source": "必要条件",
    "target": "充分必要条件",
    "weight": 0.7
  },
  {
    "source": "数列有界",
    "target": "数列收敛",
    "weight": 0.8
  },
  {
    "source": "函数局部有界",
    "target": "函数极限存在",
    "weight": 0.8
  },
  {
    "source": "函数局部无界",
    "target": "无穷大",
    "weight": 0.8
  },
  {
    "source": "左极限",
    "target": "函数极限存在",
    "weight": 0.9
  },
  {
    "source": "右极限",
    "target": "函数极限存在",
    "weight": 0.9
  },
  {
    "source": "函数极限",
    "target": "函数连续性",
    "weight": 0.9
  },
  {
    "source": "极限的计算",
    "target": "无穷小的比较",
    "weight": 0.9
  },
  {
    "source": "基本极限公式",
    "target": "无穷小的比较",
    "weight": 0.85
  },
  {
    "source": "左右极限",
    "target": "间断点分类",
    "weight": 0.9
  },
  {
    "source": "极限的计算",
    "target": "间断点分类",
    "weight": 0.8
  },
  {
    "source": "复合函数",
    "target": "复合函数的定义域",
    "weight": 0.9
  },
  {
    "source": "基本初等函数的性质",
    "target": "复合函数的定义域",
    "weight": 0.8
  },
  {
    "source": "解不等式",
    "target": "复合函数的定义域",
    "weight": 0.7
  },
  {
    "source": "函数的概念",
    "target": "分段函数",
    "weight": 0.8
  },
  {
    "source": "向量及其线性运算",
    "target": "数量积 向量积 混合积",
    "weight": 0.9
  },
  {
    "source": "向量及其线性运算",
    "target": "平面及其方程",
    "weight": 0.8
  },
  {
    "source": "数量积 向量积 混合积",
    "target": "平面及其方程",
    "weight": 0.9
  },
  {
    "source": "平面及其方程",
    "target": "空间直线及其方程",
    "weight": 0.9
  },
  {
    "source": "向量及其线性运算",
    "target": "曲面及其方程",
    "weight": 0.7
  },
  {
    "source": "曲面及其方程",
    "target": "空间曲线及其方程",
    "weight": 0.85
  },
  {
    "source": "空间直线及其方程",
    "target": "空间曲线及其方程",
    "weight": 0.7
  },
  {
    "source": "多元函数的基本概念",
    "target": "偏导数",
    "weight": 0.95
  },
  {
    "source": "偏导数",
    "target": "多元复合函数的求导法则",
    "weight": 0.9
  },
  {
    "source": "全微分",
    "target": "多元复合函数的求导法则",
    "weight": 0.8
  },
  {
    "source": "多元复合函数的求导法则",
    "target": "隐函数的求导公式",
    "weight": 0.95
  },
  {
    "source": "偏导数",
    "target": "方向导数与梯度",
    "weight": 0.9
  },
  {
    "source": "偏导数",
    "target": "多元函数微分学的几何应用",
    "weight": 0.85
  },
  {
    "source": "隐函数的求导公式",
    "target": "多元函数微分学的几何应用",
    "weight": 0.8
  },
  {
    "source": "空间直线及其方程",
    "target": "多元函数微分学的几何应用",
    "weight": 0.85
  },
  {
    "source": "曲面及其方程",
    "target": "多元函数微分学的几何应用",
    "weight": 0.85
  },
  {
    "source": "偏导数",
    "target": "多元函数的极值及其求法",
    "weight": 0.9
  },
  {
    "source": "全微分",
    "target": "二元函数的泰勒公式",
    "weight": 0.85
  },
  {
    "source": "多元函数的极值及其求法",
    "target": "最小二乘法",
    "weight": 0.8
  },
  {
    "source": "多元函数的基本概念",
    "target": "二重积分的概念与性质",
    "weight": 0.85
  },
  {
    "source": "曲面及其方程",
    "target": "二重积分的计算法",
    "weight": 0.8
  },
  {
    "source": "二重积分的概念与性质",
    "target": "二重积分的计算法",
    "weight": 0.95
  },
  {
    "source": "二重积分的计算法",
    "target": "三重积分",
    "weight": 0.95
  },
  {
    "source": "向量概念",
    "target": "向量的线性运算",
    "weight": 0.9
  },
  {
    "source": "向量代数",
    "target": "空间解析几何",
    "weight": 0.85
  },
  {
    "source": "向量的线性运算",
    "target": "空间解析几何",
    "weight": 0.7
  },
  {
    "source": "向量的加减法",
    "target": "向量的线性运算",
    "weight": 0.9
  },
  {
    "source": "向量的数乘",
    "target": "向量的线性运算",
    "weight": 0.9
  },
  {
    "source": "向量的加减法",
    "target": "向量相等的定义",
    "weight": 0.8
  },
  {
    "source": "向量相等的定义",
    "target": "向量共线(平行)条件",
    "weight": 0.85
  },
  {
    "source": "向量共线(平行)条件",
    "target": "向量法证几何问题",
    "weight": 0.9
  },
  {
    "source": "向量的线性运算",
    "target": "向量的定比分点",
    "weight": 0.85
  },
  {
    "source": "向量的概念",
    "target": "向量的加减法",
    "weight": 0.9
  },
  {
    "source": "向量的概念",
    "target": "向量的数乘",
    "weight": 0.9
  },
  {
    "source": "向量的加减法",
    "target": "向量的坐标运算",
    "weight": 0.85
  },
  {
    "source": "向量的数乘",
    "target": "向量的坐标运算",
    "weight": 0.85
  },
  {
    "source": "向量的坐标表示",
    "target": "向量的坐标运算",
    "weight": 0.95
  },
  {
    "source": "向量的模",
    "target": "单位向量",
    "weight": 0.9
  },
  {
    "source": "向量数乘",
    "target": "单位向量",
    "weight": 0.8
  },
  {
    "source": "单位向量",
    "target": "平行向量",
    "weight": 0.85
  },
  {
    "source": "空间直角坐标系",
    "target": "卦限",
    "weight": 0.9
  },
  {
    "source": "空间直角坐标系",
    "target": "坐标面与坐标轴上的点",
    "weight": 0.9
  },
  {
    "source": "空间直角坐标系的概念",
    "target": "坐标面上的点的坐标特征",
    "weight": 0.9
  },
  {
    "source": "空间直角坐标系的概念",
    "target": "坐标轴上的点的坐标特征",
    "weight": 0.9
  },
  {
    "source": "坐标面上的点的坐标特征",
    "target": "点关于坐标面的对称",
    "weight": 0.8
  },
  {
    "source": "坐标轴上的点的坐标特征",
    "target": "点关于坐标轴的对称",
    "weight": 0.8
  },
  {
    "source": "空间直角坐标系的概念",
    "target": "点关于原点的对称",
    "weight": 0.85
  },
  {
    "source": "点关于坐标面的对称",
    "target": "点关于坐标轴的对称",
    "weight": 0.6
  },
  {
    "source": "点关于坐标面的对称",
    "target": "点关于原点的对称",
    "weight": 0.6
  },
  {
    "source": "向量的模",
    "target": "方向余弦",
    "weight": 0.9
  },
  {
    "source": "方向余弦",
    "target": "方向角",
    "weight": 0.95
  },
  {
    "source": "方向余弦",
    "target": "向量与坐标轴或坐标面的关系",
    "weight": 0.9
  },
  {
    "source": "向量的模",
    "target": "向量在轴上的投影",
    "weight": 0.85
  },
  {
    "source": "方向角",
    "target": "向量在轴上的投影",
    "weight": 0.85
  },
  {
    "source": "向量的模",
    "target": "向量的投影",
    "weight": 0.9
  },
  {
    "source": "向量的坐标表示",
    "target": "向量的线性运算",
    "weight": 0.9
  },
  {
    "source": "向量的坐标表示",
    "target": "向量的投影",
    "weight": 0.85
  },
  {
    "source": "向量的投影",
    "target": "向量的分向量",
    "weight": 0.85
  },
  {
    "source": "向量的线性运算",
    "target": "向量的分向量",
    "weight": 0.8
  },
  {
    "source": "向量的坐标表示",
    "target": "数量积",
    "weight": 0.85
  },
  {
    "source": "向量的坐标表示",
    "target": "向量积",
    "weight": 0.85
  }
]