12.08 - [Hand out Concept Check 13 sheet[Hand out cover...

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[Hand out Concept Check 13 sheet] [Hand out cover sheet for exam and read it aloud] The exam will focus on chapters 12 and 13. You may use a five-page “cheat-sheet”, but it must be created by you; you cannot photocopy reference books or print things out from the web. I will be here before 12; as soon as everybody’s here, we’ll start the exam. We can stay in PA 408 till 1 p.m; after that we’ll have to move to PA 407. Concept check for Chapter 13: 10, 12 Return HW Questions about group work from yesterday? Group Work: Use the Divergence Theorem to evaluate the integral ∫∫ S = B ( x + y 2 +2 z ) dS , where B is the solid ball x 2 + y 2 + z 2 4. [Put this on board so students can copy it.] ..?. . To apply the Divergence Theorem, we need to guess a vector field F such that F n = x + y 2 + 2 z .

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Set F = P i + Q j + R k . Since the outward unit normal on S is n = ½ ( x i + y j + z k ), we have ½ xP = x , ½ y Q = y 2 , and ½ z R = 2 z . Thus we need
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This note was uploaded on 02/13/2012 for the course MATH 241 taught by Professor Staff during the Fall '11 term at UMass Lowell.

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12.08 - [Hand out Concept Check 13 sheet[Hand out cover...

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