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ps5-2010 - 18.02A Problem Set 5 IAP 2010 due Friday Jan 8...

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18.02A Problem Set 5 – IAP 2010 due Friday Jan. 8, 11:45 in 2-106 Part I (20 points) Lecture 40. Mon. Jan. 4 Vector fields and line integrals in the plane. Work. Read: Notes V2, Simmons 21.1 Work: 4A-3bd, 4; 4B-1bef, 2, 3 Lecture 41. Tues. Jan. 5 Gradient fields, conservative fields, path-independence; Fundamental Theorem of Calculus for line integrals. Read: 21.2 to p.762 Work: 4C-1,2,3 Lecture 42. Wed. Jan. 6. Criterion for conservative fields; potential functions. Read: Notes V2 Work: 4C-5a, 6ab (do all 3 by Method 1 and Method 2) Lecture 43. Thurs. Jan.7 Green’s Theorem (tangential form) Read: 21.3 to middle p. 768 Work: 4D-1bc, 2, 3, 5. Lecture 44. Friday Jan.8 Flux; Green’s theorem in normal form Read: Notes V3, V4 Part II (30 points) Directions. Try each problem alone for 15 minutes. If you subsequently collaborate, solutions must be written up independently. It is illegal to consult problem sets from previous semesters. With each problem is the day it can be done. Problem 1. (Tues. 6pts: 3+3) Consider F = (4 xy + y 2 +2) i + (2 x 2 +2 xy + y 2 ) j . Find a potential for F in two ways: a) the algebraic method, and b) the integration method.
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