# HW3 - ⎧ < < ≤ < ≤ < ≤ < = 1 4 3 4 3...

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Homework #3 Due: Tuesday, February 24, 2009 Compute the Fourier coefficients, and expand in Fourier series the following 1-periodic functions. Note : Use of Matlab (or any other software) is not permitted. 1. () x 2 1 2 π , for 1 0 < < x 2. () 2 2 6 6 1 6 x x + , for 1 0 < < x 3. () 3 2 3 2 3 3 x x x + , for 1 0 < < x 4. () 4 3 2 4 30 60 30 1 90 x x x + , for 1 0 < < x 5. < < = < < = 1 2 1 0 2 1 2 1 x 0 ) ( x for x for a for x x f What should a be so that the Fourier series converges to f(x) for every 0<x<1 ? 6. < < < < < = 1 4 3 4 4 4 3 2 1 2 4 2 1 4 1 4 2 4 1 0 4 ) ( x x x x x x x x x f Is the Fourier series convergent for every 0<x<1 ?

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Unformatted text preview: ⎧ < < ≤ < ≤ < ≤ < = 1 4 3 4 3 2 1 1 2 1 4 1 4 1 1 ) ( x x x x x f Is the Fourier series convergent to f(x) for every 0<x<1 ? In the following three problems the functions are extended by periodicity outside the interval of definition. 8. ) 2 sin( xs π , for 2 1 2 1 < < − x and 1 < < s 9. ) 2 cos( xs , for 2 1 2 1 < < − x and 1 < < s 10. ixs e 2 , for 2 1 2 1 < < − x and 1 < < s Total : 10 pts (1 point each)...
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## This note was uploaded on 03/21/2010 for the course MATH 464 taught by Professor Staff during the Spring '08 term at Maryland.

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HW3 - ⎧ < < ≤ < ≤ < ≤ < = 1 4 3 4 3...

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