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fix: Proofread Part India (line integrals of vector fields) - #89

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Jun 19, 2026
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Closes #66.

Proofread all the src/*.typ files included under Part India (vecfield.typ, gcd.typ, work.typ, ftcgreen.typ, 2dflux.typ, lineex.typ, mt3.typ). Found and fixed the following minor issues:

src/vecfield.typ

  • Word-choice error: a whirlpool swirls around its vortex, not its "vertex".
  • Word-choice error: the downstream function increases as you get farther from the head of the river (not "the bank", which refers to the side rather than position along the river).
  • Grammar: "I want tell you" → "I want to tell you".
  • Grammar: "the gradient creates into a vector field" → "the gradient creates a vector field".
  • Duplicate word: "what this means for each individual red arrow means" → "...for each individual red arrow".

src/work.typ

  • Typo: "Then notation" → "The notation".
  • Calculation error: in the bare-hands work example, the vector field was evaluated as F(0, 1-2t) but the parametrization is r(t) = (1-2t, 0), so it should be F(1-2t, 0). (The displayed final vector (0, 3-6t) was already correct, only the intermediate function-application notation had the arguments swapped.)

src/ftcgreen.typ

  • The prose said to "integrate ... from 0 to π/2" while the displayed integral correctly used bounds 0 to π — fixed the prose to match.
  • The displayed antiderivative -cos(2t) - cos(t) was missing a factor of 1/4 and had the wrong sign on cos(t); corrected to -cos(2t)/4 + cos(t), which integrates the given integrand correctly and yields the stated answer of -2.
  • Grammar: "will always just equal to $c$" → "will always just equal $c$".

src/2dflux.typ

  • In a flux example, the rotated vector field $vec(-q,p)$ was mislabeled as vec(cos(t)^2, sin(t)^2) (which is actually $vec(p,q)$); corrected to vec(-sin(t)^2, cos(t)^2), and fixed the subsequent dot-product expansion to match. The final boxed answer was unaffected.

No large mathematical errors were found; all final boxed answers in this part were independently re-derived and confirmed correct.

🤖 Generated with Claude Code


Generated by Claude Code

- vecfield.typ: fix grammar ("want tell" -> "want to tell", "creates
  into" -> "creates", duplicate "means"), and correct word choice
  ("vertex" -> "vortex" of a whirlpool, "bank" -> "head" for downstream
  distance)
- work.typ: fix typo "Then notation" -> "The notation", and fix a
  vector field evaluation that had its arguments swapped
  (F(0, 1-2t) -> F(1-2t, 0))
- ftcgreen.typ: fix incorrect integration bounds stated in prose
  (0 to pi/2 -> 0 to pi) and a wrong antiderivative coefficient
  (-cos(2t) - cos(t) -> -cos(2t)/4 + cos(t)); fix grammar "equal to"
  -> "equal"
- 2dflux.typ: fix a mislabeled rotated vector field
  (vec(cos(t)^2, sin(t)^2) -> vec(-sin(t)^2, cos(t)^2)) so the dot
  product computation is internally consistent

Closes #66.
@vEnhance
vEnhance merged commit 33c8d1e into main Jun 19, 2026
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@vEnhance vEnhance added the proofreading-campaign Systematically proofread the textbook label Jun 19, 2026
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Proofread Part India

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