Differential Equations Lecture Work Solutions 36

Differential Equations Lecture Work Solutions 36 - 3.4...

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3.4 Relationship to Least Squares 3.5 Convergence 3.6 Fourier Cosine and Sine Series Problems 1. For each of the following functions i. Sketch f ( x ) ii. Sketch the Fourier series of f ( x ) iii. Sketch the Fourier sine series of f ( x ) iv. Sketch the Fourier cosine series of f ( x ) a. f ( x )= xx < 0 1+ xx> 0 b. f ( x e x c. f ( x )=1+ x 2 d. f ( x 1 2 x +1 2 <x< 0 x 0 2 2. Sketch the Fourier sine series of f ( x )=cos π L x. Roughly sketch the sum of the ±rst three terms of the Fourier sine series. 3. Sketch the Fourier cosine series and evaluate its coefficients for f ( x
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.

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