f02q3sol - 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 FALL 2002 QUIZ 3 SOLUTIONS PROBLEM 1 a) The graph looks likc a symmctric buttcrfly. It is periodic with no discontinuitics (but has kinks at x = 0 and x = k7r, whcrc the slopc jumps). . . . . b) dfldz: Thc right half of the graph becomes -ee": now it's an odd buttcrfly. 8 f/dx2: Back to thc cvcn buttcrfly with 6-functions -26 (2) and 2ee"6 (x - 71). The 6-functions comc from jumps in dfldx. c) From b) -- d2f + f = 26 (2) - 2ee"6 (z - T) dx2 If f (x) = CckeikZ thcn (recall 6 (x) = C eik"; 5 + ik): Equate cocfficicnts of likc terms: (k2 + 1) Ck = - 1 (1 - (-I)~ee") 7r The solution of this algebraic cquation is thc samc answer as bcforc,
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f02q3sol - MIT OpenCourseWare http:/ocw.mit.edu 18.085...

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