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Examples of Fourier Expansions of FunctionsSome Remarks
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algebraic amplitude angle angular frequency applied mathematics arbitrary constants axis beam Bessel function boundary conditions Chap complex numbers compute const constant coefficients convergent coordinates corresponding cosh curve defined definite integral deflection denotes derivative determine displacement electromotive force elements equal equation of motion evaluated example expression finite formula Fourier series fundamental Gamma function given harmonic Hence imaginary infinite initial conditions inverse transform Jordan's lemma Laplace transform Laplace's equation Laplacian Laplacian transform Legendre polynomials Let us consider line integral linear differential equations mass matrix maximum method multiply natural frequencies obtain Operational Calculus oscillations particle plane polynomial problem quantities region represents satisfies scalar Show shown in Fig sinh solution solve Substituting surface table of transforms temperature theorem theory unit length values vanish vector velocity vibration wave write written zero