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).