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q118085f05

# q118085f05 - 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 12, 2005 Professor Strang 1) (40 pts.) Here is a network with 9 numbered nodes and then separately the 12 edges. 7 8 9 5 8 12 4 6 7 11 1 2 3 3 4 5 6 9 10 1 2 (a) What is the shape of the incidence matrix A ? What is its 4th row ? (b) What is the 5th column of A ? What is the (5 , 5) entry in A T A ? Write the whole 5th row of A T A . (c) How many independent solutions to Kirchhoff’s Law A T w = 0 ? Find one of them . (d) Without writing down this matrix A , explain why A T A is or is not symmetric positive definite. 1 Your PRINTED name is: Grading 1 2 3
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2) (30 pts.) (a) For a hanging elastic bar, with u (0) = 0 at the top and u (0) = 0 at the bottom and elastic constant c ( x ) = 1, what is the displacement u ( x ) when a unit point load f ( x ) = ( x a ) acts at the point x = a ?
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q118085f05 - MIT OpenCourseWare http/ocw.mit.edu 18.085...

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