Differential Equations Lecture Work Solutions 26

Differential Equations Lecture Work Solutions 26 - 3...

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3 Fourier Series 3.1 Introduction 3.2 Orthogonality 3.3 Computation of Coefficients Problems 1. For the following functions, sketch the Fourier series of f ( x ) on the interval [ L, L ]. Compare f ( x ) to its Fourier series a. f ( x )=1 b. f ( x )= x 2 c. f ( x e x d. f ( x 1 2 xx< 0 3 xx> 0 e. f ( x 0 x< L 2 x 2 x> L 2 2. Sketch the Fourier series of f ( x ) on the interval [ L, L ] and evaluate the Fourier coeffi- cients for each a.
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