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fix: proofread solutions for Part Juliett - #92

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Jun 19, 2026
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Closes #69.

Proofread src/sol-juliett.typ (solutions for Part Juliett). Found and fixed two issues:

  • exer-flux-sealing: clarified an ambiguous sentence that said "We orient the normal vector pointing upward" without naming which surface; the orientation choice being described is for $cal(S)_"lid"$, not $cal(S)$ (whose orientation is already fixed by the problem statement). Specified the surface explicitly.
  • exer-gravity-div2: the divergence theorem identity had the two surface-flux terms subtracted in the wrong order. Given that $cal(S)1$'s normal points away from $cal(T)$ (matching the outward-from-$cal(T)$ orientation) while $cal(S)2$'s normal points toward $cal(T)$ (opposite the outward-from-$cal(T)$ orientation), correctly applying the divergence theorem gives iint_(S1) - iint_(S2) = iiint_T div, not iint_(S2) - iint_(S1) as written. I verified the corrected sign by direct computation with a radial test field ($bf(F) = chevron.l x,y,z chevron.r$, $div bf(F) = 3$) on concentric spheres of radius 1 and 2: $32pi - 4pi = 28pi$ matches $iiint_T 3 dif V = 28pi$, confirming iint_(S1) - iint_(S2) is the correct order. Since this exercise has $div bf(G) = 0$, the final boxed conclusion ($oiint(S_1) = oiint(S_2)$) is unaffected either way, but the intermediate identity as stated was incorrect in general.

No other mathematical errors were found; the remaining solutions (flux through $x^3+y^4=e^z$, divergence-to-Green, Stokes-to-Green) were independently re-derived and check out correctly.

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 file — no issues.

Generated by Claude Code

Closes #69.

Proofread src/sol-juliett.typ (solutions for Part Juliett). Found and
fixed two issues:

- exer-flux-sealing: clarified an ambiguous sentence that said "We
  orient the normal vector pointing upward" without naming which
  surface; the orientation choice being described is for
  cal(S)_lid, not cal(S) (whose orientation is fixed by the problem
  statement). Specified the surface explicitly.
- exer-gravity-div2: the divergence theorem identity had the two
  surface-flux terms subtracted in the wrong order. Given that
  cal(S)_1's normal points away from cal(T) (matching the
  outward-from-T orientation) while cal(S)_2's normal points toward
  cal(T) (opposite the outward-from-T orientation), applying the
  divergence theorem correctly gives
  iint_(S1) - iint_(S2) = iiint_T div, not iint_(S2) - iint_(S1) as
  written. Verified by direct computation with a radial test field
  (F = <x,y,z> on concentric spheres of radius 1 and 2) that the
  corrected sign is the one consistent with the divergence theorem.
  Since this exercise has div G = 0, the final boxed conclusion
  (oiint_S1 = oiint_S2) is unaffected either way, but the
  intermediate identity as stated was incorrect for fields with
  nonzero divergence.

No other mathematical errors were found; the remaining solutions
(flux through x^3+y^4=e^z, divergence-to-Green, Stokes-to-Green) were
independently re-derived and check out correctly.

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 file -- no issues.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_012MAUxHgBxnMLHWiU62jeRR
@vEnhance
vEnhance merged commit ba90bfb 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 solutions for Part Juliett

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