pset3 - Physics (PHZ) 3113 Mathematical Physics Florida...

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Physics (PHZ) 3113 Mathematical Physics Florida Atlantic University Fall, 2010 Problem Set III Due: Thursday, 16 September 2010 1. (Problems 7.5.2 and 10, pp. 354–355) Sketch several periods of the functions whose values on the fundamental interval - π < x < π are given by the following. f (a) ( x ) := 0 - π < x < 0 1 0 < x < π/ 2 0 π/ 2 < x < π and f (b) ( x ) := ( π + x - π < x < 0 π - x 0 < x < π. Expand each in a Fourier sine-cosine series. 2. (Problems 7.7.1 and 7, pp. 360 and 354–355) Sketch several periods of the functions whose values on the fundamental interval - π < x < π are given by the following. f (a) ( x ) := ( 1 - π < x < 0 0 0 < x < π and f (b) ( x ) := ( 0 - π < x < 0 x 0 < x < π. Expand each in a Fourier exponential series. 3. (Problems 7.8.12 and 14, p. 363) a. Consider the function f ( x ) := e x restricted to the fundamental interval I := - π < x < π , and then extended to the real line again periodically. Sketch several periods of this function and calculate a Foruier series for it. b. Repeat the previous part for the interval
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