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fix: Proofread Part Juliett (flux integrals of vector fields over a surface) - #91

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Closes #68.

Proofread src/flux.typ, src/divthm.typ, src/badstokes.typ (the files included under Part Juliett). Found and fixed:

  • src/flux.typ: incomplete sentence "explain what the adjective 'oriented'." was missing "means".
  • src/flux.typ: in the sphere-orientation example, "either points straight towards the center of from $P$, or away from the center of $P$" was garbled; simplified to "either points straight towards the center, or away from the center."
  • src/flux.typ: the same example parametrizes "the hemisphere" (sphere with $z>0$) but gave the bounds as $0 <= phi <= pi$ (the whole sphere) in both orderings; corrected to $0 <= phi <= pi/2$.
  • src/flux.typ: in the $z = x^3+y^3$ flux sample, the displayed equation vec(3x^2,3y^2,-1) = vec(-3x^2,-3y^2,1) falsely equated a vector with its own negation; removed the erroneous first (negated) vector, since the dot product computed immediately afterward uses the non-negated one.
  • src/flux.typ: in the cylinder flux sample, 490 dot (3 pi + 8 pi) should be 490 dot (3 pi + 5 pi) to match $int cos^2 = int sin^2 = pi$ (the final boxed answer of $3920 pi$ was already correct).
  • src/flux.typ: in the spherical-coordinates hemisphere sample, a displayed integral dropped the $cos phi$ factor present in the line immediately before and the line immediately after it.
  • src/flux.typ: in the point-mass-gravity flux sample, the dot-product line used $bf(F)$ instead of $bf(G)$ (the vector field is named $G$ in this example), and the general surface-area formula was given as "$R^2 pi$" instead of the correct "$4 R^2 pi$" (the actual computation in the same sample already used the correct $4 R^2 pi$).
  • src/divthm.typ: a missing \ line break caused two rows of an aligned equation to run together.
  • src/divthm.typ: moved a stray period to match the #boxed[...]. #qedhere convention used everywhere else in the file.
  • src/badstokes.typ: the classical Stokes' theorem statement said "Suppose $cal(S)$ is the boundary of an oriented surface $cal(S)$", which is self-referential nonsense; corrected to "Suppose $cal(C)$ is the boundary of an oriented surface $cal(S)$", consistent with the definition of compatible orientations given just above it.

No large mathematical errors were found beyond the sign/factor slips above.

Test plan

  • Installed typst 0.15.0 plus the @local/evan:1.0.0 package (from vEnhance/dotfiles) and the required @preview deps (gentle-clues, linguify), generated placeholder SVGs standing in for the Asymptote figures (asy isn't available in this environment), then ran typst compile lamv.typ end-to-end — compiles cleanly with no errors.
  • Ran codespell on the three changed files — no issues.

Generated by Claude Code

…urface)

Closes #68.

Proofread src/flux.typ, src/divthm.typ, src/badstokes.typ (the files
included under Part Juliett). Found and fixed:

- src/flux.typ: incomplete sentence "explain what the adjective
  'oriented'." was missing "means".
- src/flux.typ: in the sphere-orientation example, "either points
  straight towards the center of from P, or away from the center of
  P" was garbled; simplified to "either points straight towards the
  center, or away from the center."
- src/flux.typ: the same example parametrizes "the hemisphere" (sphere
  with z > 0) but gave the bounds as 0 <= phi <= pi (the whole sphere)
  in both orderings; corrected to 0 <= phi <= pi/2.
- src/flux.typ: in the z = x^3+y^3 flux sample, the displayed equation
  "vec(3x^2,3y^2,-1) = vec(-3x^2,-3y^2,1)" falsely equated a vector
  with its own negation; removed the erroneous first (negated) vector,
  since the dot product computed immediately afterward uses the
  non-negated one.
- src/flux.typ: in the cylinder flux sample, "490 dot (3 pi + 8 pi)"
  should be "490 dot (3 pi + 5 pi)" to match int cos^2 = int sin^2 = pi
  (the final boxed answer of 3920 pi was already correct).
- src/flux.typ: in the spherical-coordinates hemisphere sample, a
  displayed integral dropped the cos(phi) factor present in the line
  immediately before and the line immediately after it.
- src/flux.typ: in the point-mass-gravity flux sample, the dot-product
  line used bf(F) instead of bf(G) (the vector field is named G in
  this example), and the general surface-area formula was given as
  "R^2 pi" instead of the correct "4 R^2 pi" (the actual computation
  in the same sample already used the correct 4 R^2 pi).
- src/divthm.typ: a missing "\" line break caused two rows of an
  aligned equation to run together.
- src/divthm.typ: moved a stray period to match the "#boxed[...].
  #qedhere" convention used everywhere else in the file.
- src/badstokes.typ: the classical Stokes' theorem statement said
  "Suppose cal(S) is the boundary of an oriented surface cal(S)",
  which is self-referential nonsense; corrected to "Suppose cal(C) is
  the boundary of an oriented surface cal(S)", consistent with the
  definition of compatible orientations given just above it.

No large mathematical errors were found beyond the sign/factor slips
above.

## Test plan
- Installed typst 0.15.0 plus the @local/evan:1.0.0 package (from
  vEnhance/dotfiles) and the required @Preview deps (gentle-clues,
  linguify), generated placeholder SVGs standing in for the Asymptote
  figures (asy isn't available in this environment), then ran
  `typst compile lamv.typ` end-to-end — compiles cleanly with no
  errors.
- Ran codespell on the three changed files — no issues.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_019s4SnXrKoKvtcpmmTmCQLL
@vEnhance
vEnhance merged commit 15d25d2 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 Juliett

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