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The Method of Greens Functions
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applied approximate associated assume beam becomes Bessel boundary conditions boundary value problem called Chapter coefficients column consider constant continuous converges corresponding cosh deduce defined depends derivative described determine difference differential discussed displacement domain eigenfunctions eigenvalue problem eigenvalues equation EXAMPLE Exercises exists expression Figure Finally finite fixed force formal formula Fourier series given Green's function heat Hence homogeneous identity independent infinite initial integral interval involving Laplace transform leads linear load mathematical method nonhomogeneous numerical obtain operator orthogonal particular periodic physical positive potential prescribed relation remaining require respectively result satisfy separation simply sinh solution solve steady-state string substitution technique temperature temperature distribution theorem theory tion transform unit variables wave write yields zero