q218085f03sol

q218085f03sol - MIT OpenCourseWare http:/ocw.mit.edu 18.085...

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MIT OpenCourseWare http://ocw.mit.edu 18.085 Computational Science and Engineering I Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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18.085 Prof. Strang Quiz 2 SOLUTIONS November 7, 2003 1 2 3 Your name is: Grading Total 1) (36 pts.) (a) For d 2 u = δ ( x a ) with u (0) = u (1) = 0, the solution is linear on dx 2 both sides of x = a (graph = triangle from two straight lines). What is wrong with the next sentence ? Integrating both sides of u = δ ( x a ), from x = 0 to x = 1, the area under the triangle graph is 1. The base is 1 so the height must be u max = 2. (b) If u ( x, a ) is the true solution to that standard problem in part (a), and the load point x = a approaches x = 1, what function does the solution u approach ? Give a physical reason for your answer or a math reason or both. Integrating δ ( x a ) does give 1. But the area under the graph of u ( x ) is u ( x ) dx and not u ( x ) dx . (The
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This note was uploaded on 04/12/2011 for the course MATH 18.085 taught by Professor Staff during the Fall '10 term at MIT.

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q218085f03sol - MIT OpenCourseWare http:/ocw.mit.edu 18.085...

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