quiz1sol_f08

quiz1sol_f08 - 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 Quiz 1 October 7, 2008 Professor Strang Your PRINTED name is Student Number Grading 1 2 3 4 1. Start with the equation -$(c(x)&) = 1. The fixed-hed boundary conditions are dx. u(0) = 0 = u(1). The function c(x) Jumps from 1to 2 at x = $: c(x) = 1for x 5 i c(x) = 2 for x > a. (a) Take Ax = and uo = uq = 0. Create a difference equation ATCAu = f that models this problem. What are the shapes of A and C? What are those matrices? Hint from review session: The FREEFREE matrix is 4 by 5. Solution: The fixed-fixed matrix A removes the boundary columns 1 and 5 of the free-free matrix An. So A is 4 by 3 and C is 4 by 4: (b) Multiply ATCA to find K. Circle one of these properties. The matrix K is (positive definite) (only positive semidefinite) (indefinite) Prove your statement from the numbers in
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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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quiz1sol_f08 - MIT OpenCourseWare http:/ocw.mit.edu 18.085...

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