quiz318085f04

quiz318085f04 - 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 3 December 2, 2004 Professor Strang Your name is: Grading 1. 2. 3. Thank you for taking 18.085 ! I hope to see you in 18.086 !! 1) (40 pts.) This question is about 2 π -periodic functions . d l e ilx (a) Suppose f ( x )= c k e ikx and g ( x )= . Substitute for f and g and integrate to find the coefficients q n in this convolution: ± 2 π ± 2 π ² h ( x )= f ( t ) g ( x t ) dt = f ( x t ) g ( t ) dt = q n e inx . 0 0 (b) Compute the coefficients c k for the function 1f o r 0 x 1 f ( x )= 0f o r 1 x 2 π 2 ? What is the decay rate of these c k ?Wha t i s | c k | (c) Keep that f ( x ) in parts (c)–(d). If g ( x ) also has a jump, will the convolution h ( x ) have a jump ? Compare the decay rates of the d ’s and q
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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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quiz318085f04 - MIT OpenCourseWare http/ocw.mit.edu 18.085...

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