Applied Mathematics for Engineers and Physicists |
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algebraic amplitude angular frequency arbitrary constants axis Bessel function boundary conditions c₁ Chap column complex numbers const convergent coordinates cosh curve defined deflection denotes derivative determine displacement e-at electromotive force elements equal equation of motion evaluated example expansion expression finite force Fourier series fundamental given harmonic Hence infinite initial conditions inverse transform Laplace transform Laplace's equation Laplacian Laplacian transform Let us consider line integral linear differential equations mass matrix maximum method multiply natural frequencies obtain Operational Calculus oscillations particle plane polynomial positive potential problem quantities roots satisfies scalar shown in Fig sinh solution solve Substituting surface table of transforms temperature theorem theory unit length values vanish variable vector velocity vibration write z₁ zero ди ду дх მყ