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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 ) = x x < 0 1 + x x > 0 b. f ( x ) = e x c. f ( x ) = 1 + x 2 d. f ( x ) = 1 2 x + 1 2 < x < 0 x 0 < x < 2 2. Sketch the Fourier sine series of f ( x ) = cos π L x. Roughly sketch the sum of the first three terms of the Fourier sine series. 3. Sketch the Fourier cosine series and evaluate its coeﬃcients for f ( x ) =
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