Lecture Notes for Numerical Analysis with Python

Third Edition (2026) · Stephen E. Moore · Department of Mathematics, University of Cape Coast, Ghana

🌐 Author's website: https://moorestephen.info/ 📘 Download the book (PDF): Numerical_Analysis_with_Python_3rd_Edition.pdf

This repository contains the book and all of its Python programs. The notes were written for MAT 407: Numerical Analysis I, a final-year undergraduate course at the University of Cape Coast, and they also aim to prepare students for graduate study.

About the book

Numerical analysis is the study of algorithms for the problems of continuous mathematics: solving equations, solving linear systems, approximating functions and data, and differentiating and integrating numerically. For every algorithm the book asks three questions: Does it converge? How fast? How reliable is it in floating-point arithmetic?

Every method is derived, analysed (with proofs of the main theorems) and implemented in Python. Every Python listing in the book has been run, and the output printed beneath it is the real output of the program in this repository.

Each chapter contains:

• Learning objectives and a chapter summary
• worked examples by hand and in Python
• highlighted Key Concept boxes (the ideas you must understand)
• Historical Notes on the people and problems behind the mathematics
• Caution boxes on common mistakes and pitfalls of computer arithmetic
• Towards Graduate Studies boxes linking each topic to advanced mathematics
• exercises after every section, tagged Theory, Python and ★ Graduate, with answers to selected exercises in Appendix B

Contents and code

Part	Chapter	Code folder	Programs
I. Foundations	1. Introduction to Python Programming	code/ch01	basics, vectors, matrices, loops, functions, plotting, the bungee jumper (Euler's method)
	2. Number Systems	code/ch02	base conversion, integers and two's complement
	3. Floating-Point Arithmetic and Round-off Errors	code/ch03	IEEE 754 bits, machine epsilon, k-digit arithmetic, cancellation, conditioning, summation, the Patriot missile
II. Nonlinear equations	4. Solutions of Nonlinear Equations	code/ch04	bisection, fixed point, Newton, secant, regula falsi, Aitken/Steffensen, Newton fractal, SciPy root finders
	5. Systems of Nonlinear Equations	code/ch05	Newton for systems, Lorenz equilibria, Broyden, scipy.optimize
III. Linear systems	6. Direct Methods: LU, Cholesky, QR	code/ch06	Gaussian elimination, pivoting, LU, tridiagonal (Thomas), Cholesky, Gram–Schmidt QR
	7. Iterative Methods for Linear Systems	code/ch07	Jacobi, Gauss–Seidel, SOR, steepest descent, conjugate gradients, 2D Poisson problem
	8. Norms, Condition Numbers and Error Estimates	code/ch08	vector and matrix norms, condition numbers, iterative refinement
IV. Approximation	9. Polynomial Interpolation	code/ch09	Vandermonde, Lagrange, divided differences, Runge's phenomenon, splines
	10. Least Squares and Orthogonal Polynomials	code/ch10	line fitting, normal equations vs QR, exponential fits (population of Ghana), Legendre and Chebyshev polynomials
	11. Approximation by Rational Functions	code/ch11	Padé approximation, Chebyshev rational approximation
V. Numerical calculus	12. Numerical Differentiation	code/ch12	finite differences, choice of step size, Richardson extrapolation, noisy data, complex step
	13. Numerical Integration and Adaptive Quadrature	code/ch13	Newton–Cotes, composite rules, Romberg, Gauss–Legendre, adaptive Simpson

Appendix A of the book is a Python quick reference with MATLAB/Octave equivalents.

Each program code/chNN/name.py is self-contained. The file code/chNN/name.out next to it contains the output printed in the book, so you can check your results against it.

Getting started

You need Python 3 with NumPy, SciPy and Matplotlib.

• Easiest: install Anaconda, which includes everything.
• No installation: open Google Colab, upload a .py file (or paste its contents into a cell) and run it.
• With pip:

git clone https://github.com/moorekwesi/numerical-analysis-with-python.git
cd numerical-analysis-with-python
pip install -r requirements.txt

Run a single program, for example Newton's method from Chapter 4:

python code/ch04/newton.py

Programs that draw figures save them as PDF/PNG files in the folder you run them from. To run every program in the book and regenerate all outputs and figures (in figures/):

python run_all.py          # all chapters
python run_all.py ch04     # only Chapter 4

How to learn from this repository

1. Read a section of the book with the corresponding program open.
2. Run the program and compare your output with the .out file.
3. Change something: the function, the starting value, the tolerance, the step size. Predict what will happen first, then check. This is how numerical analysis is really learned.
4. Attempt the Python exercises at the end of each section; most of them start from one of these programs.

Editions

Edition	Year
First edition	2022
Second edition	2024
Third edition	2026

Citing the notes

S. E. Moore, Lecture Notes for Numerical Analysis with Python, 3rd ed., Department of Mathematics, University of Cape Coast, Ghana, 2026. Available at https://github.com/moorekwesi/numerical-analysis-with-python

Licence

You are free to use, share and adapt these materials, for teaching, learning or any other purpose, as long as you give credit to the author.

• The book (Numerical_Analysis_with_Python_3rd_Edition.pdf) is licensed under the Creative Commons Attribution 4.0 International Licence (CC BY 4.0).
• The Python programs (code/ and run_all.py) are licensed under the MIT Licence.

Author

Stephen E. Moore, Department of Mathematics, University of Cape Coast, Ghana Website: https://moorestephen.info/

Corrections and suggestions are welcome: please open an issue.