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fix: proofread solutions for Part Juliett - #92
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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 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
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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 forexer-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 givesiint_(S1) - iint_(S2) = iiint_T div, notiint_(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 $iiint_T 3 dif V = 28pi$, confirmingiint_(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
typst0.15.0 plus the@local/evan:1.0.0package (fromvEnhance/dotfiles) and the required@previewdeps (gentle-clues,linguify), generated placeholder SVGs standing in for the Asymptote figures (asyisn't available in this environment), then rantypst compile lamv.typend-to-end — compiles cleanly with no errors.codespellon the file — no issues.Generated by Claude Code