MATH503 Exam 1 Solns

MATH503 Exam 1 Solns - Exam#1 (Math 503) October 25 2010...

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Unformatted text preview: Exam#1 (Math 503) October 25 2010 STUDENT NAME: Instructions: The duration of the test is 50 minutes. The test consists of 3 questions and the marks are specified next to each question. Total mark = 50. Detail your calculations. No aid sheet or calculator allowed. 1) [17] (a) Verify Stokes theorem for the vector field F = y i + z j + x k where the open surface S is the upside-down paraboloid defined by z = 1- ( x 2 + y 2 ), z 0, with upward normal. (b) What condition should F satisfy to be conservative? Solution: (a) Here f = 1- ( x 2 + y 2 ) and G = F = (- 1 ,- 1 ,- 1), so ZZ S ( F ) n dS = ZZ R- G x f x- G y f y + G z dxdy =- ZZ R (2 x + 2 y + 1) dxdy =- Z 2 Z 1 (2 r cos + 2 r sin + 1) rdrd =- Z 2 h 2 3 (cos + sin ) + 1 2 i d =- Z C F t ds = Z 2 F d r d d = Z 2 sin cos - sin cos d =- Z 2 sin 2 ( ) d =- 1 2 Z 2 h 1 + cos(2 ) i d =- (b) F...
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This note was uploaded on 02/20/2011 for the course MATH 503 taught by Professor Schleiniger,g during the Fall '08 term at University of Delaware.

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MATH503 Exam 1 Solns - Exam#1 (Math 503) October 25 2010...

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