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Applications to Ordinary Differential Equations
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absolutely convergent Analytic Geometry applied arbitrary positive number beam boundary conditions boundary value problem Chapter coefficients consider continuous function Convolution Theorem corollary cosh kt D. V. Widder defined definition deflection derivatives differential system displacement driving function e~st erfc Exercises exponential order eat fact find the inverse Find the Laplace Find the transform finite discontinuities finite number FP(t frequency function F(t function of class given graph Hence illustrate implies Improper Integral Indeterminate Forms indicial response infinite interval inverse transform Laplace transform method last integral lim 1(B lim F(t lim sf(s mass motion obtain ordinary differential equations partial differential equations periodic functions polynomials positive abscissas positive constants potential Proof result satisfies sectionally continuous semi-infinite sinh kt solution function Solving for x(s string sx(s term Theorem XII transformed problem Uniform Convergence unit functions unit impulse function voltage write