q318085f03sol

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

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 =...
View Full Document

{[ snackBarMessage ]}

Page1 / 5

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online