q318085f03sol

# q318085f03sol - MIT OpenCourseWare http/ocw.mit.edu 18.085...

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Unformatted text preview: 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 . 18.085 Prof. Strang Quiz 3 Solutions December 3, 2003 Your name is: Grading 1 2 3 Total Thank you for taking 18.085, I hope you enjoyed it. 1) (35 pts.) Suppose the 2n-periodic f (x) is a half-length square wave: 1 for 0 < x < n/2 -1 for - n / 2 < x < O O elsewhere in [-n; n] (a) Find the Fourier cosine and sine coefficients ak and bk of f (x). (b) Compute J:n(f (x))' dx as a number and also as an infinite series using the a; and b;. (c) DR.4bV h GRAPH of its integral I(x). (Then dI/dx = f(x) on t,he interval [-n,n] choose the int,egration constant so I ( 0 ) = 0 . ) What are t,he Fourier coefficients 4,, and Bk of I(x)? (d) DR.4bV 4 GRAPH of the derivative D(z) = \$ from -n to n. What are t,he Fourier coefficients of D(x)? (e) If you convolve D(x) * I(x) why do you get the same answer as f (x) * f (x)? Not required t,o find that answer, just explain D * I =...
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q318085f03sol - MIT OpenCourseWare http/ocw.mit.edu 18.085...

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