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Unformatted text preview: ACM 95/100b Problem Set 5 February 16, 2009 Due by 5:00PM on 2/23/2009 All problems are worth 10 points on this set. Please deposit your problem set in the slot in 303 Firestone or upload it via Moodle. In either case please keep a copy of your problem set. Please remember to include your section number and section instructor. Collaboration is allowed on all problems but please write up the solutions yourself. Problem 1 Consider the function given by f ( x ) = (1 x 2 /L 2 ) &lt; x &lt; L. (a) Develop the Fourier sine series over the interval &lt; x &lt; L . (b) Develop the Fourier cosine series over the interval &lt; x &lt; L . (c) Develop the fully periodic Fourier series over the interval &lt; x &lt; L . ( N.B. note the interval ). (d) What is the value of each of the series at x = 0 ? Explain in each case why you get a given value. Problem 2 Compute the Fourier sine series of the function f ( x ) = cos x 1 + 2 x &lt; x &lt; How fast do the Fourier coefficients decrease with increasing n ? Explain this rate of?...
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- Winter '09
- Fourier Series, Leonhard Euler, Fourier sine series