M 311 Spring 2004
HOMEWORK SUMMARY REPORT
Chapter number: 7
Section number: 5
Exercise number: 4
Number of papers received: 2
Reviewing committee: Theta
List all participating committee members:
Jason Madsen, Xuija Zhang
Author(s) of paper(s) chosen for publication: David White
Comments:
David's paper gave a complete proof to the problem. It walked through
each step carefully aiding the reader in understanding all the concepts
being used.
GRADER'S COMMENT: Both papers wandered off the point, A surface enclosing
the volume V is divided into S_1 and S_2 by a curve C. The integrals of
curl B over S_1 and S_2 must therefore have the same magnitude, by Stokes,
but opposite sign because they are oriented oppositely. Therefore, by
Gauss the integral of div curl B over V is zero. Since V can be an
arbitrarily small region around an arbitrary point, div curl B must equal
0 everywhere.
INSTRUCTOR'S COMMENT: David has revised his paper in accordance with the
foregoing remarks, except for the "arbitrarily small and arbitrary point"
remark (needed to conclude that vanishing integral => vanishing
integrand).