Introduction to the Laplace Transform |
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Chapter I | 1 |
Transforms of Discontinuous Functions | 32 |
Chapter 4 | 43 |
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A₁ absolutely convergent Advanced Calculus Englewood algebraic equation applied boundary conditions boundary value problem Calculus Englewood Cliffs Chapter coefficients constant Convolution Theorem corollary cosh kt D. V. Widder definition driving function dx dy e-st F(t e-sto erfc Example Exercises exists exponential order eat factor find the inverse Find the transform finite discontinuities finite number function F(t given graph Hence illustrate improper integral initial conditions interval inverse transform JU(x k²)² Laplace transform Laplace transform method lim F(t lim I(B lim sf(s linear obtain ordinary differential equation partial fraction periodic functions positive number problem Proof s(s² satisfies sectionally continuous sin kt solved for x(s sx(s t₁ temperature term Theorem XI U₁ Uniform Convergence unit functions unit impulse function V₁ voltage x₁(s Y₁(t дх