Laplace Transforms and Their Applications to Differential EquationsCourier Corporation, 20 ago 2014 - 240 páginas This introduction to modern operational calculus offers a classic exposition of Laplace transform theory and its application to the solution of ordinary and partial differential equations. The treatment is addressed to graduate students in engineering, physics, and applied mathematics and may be used as a primary text or supplementary reading. Chief topics include the theorems or rules of the operational calculus, evaluation of integrals and establishment of mathematical relationships, derivation of Laplace transforms of various functions, the Laplace transform for a finite interval, and other subjects. Many problems and illustrative examples appear throughout the book, which is further augmented by helpful Appendixes. |
Otras ediciones - Ver todo
Laplace Transforms and Their Applications to Differential Equations N.W. McLachlan Vista previa restringida - 2014 |
Laplace Transforms and Their Applications to Differential Equations Norman William McLachlan Vista de fragmentos - 1970 |
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absolutely and uniformly absolutely convergent alternating Appendix applied asymptotic Bessel function boundary conditions bounded in t≥0 cable closed interval constant continuous function continuous in t≥0 convergent series converges uniformly corresponding cosh differential equation diverges dt converges e-at e-pot e-pt e-ptf(t erfc Evaluate Example f₁ Find the L.T. finitely discontinuous formula Fourier expansion h₁ Hence impulse infinite integral infinite range infinity initial conditions integral converges integral equation integral sign inverted Jo(t Ko(t Laplace transform Lerch's theorem Mellin Mellin inversion theorem monotonic obtain order of integration origin p-multiplied p²+1 positive integer Proof quiescent initially reader represents satisfied Show sinh solution Solve t)dt t₁ term by term transform equation uniformly convergent uniformly with respect valid velocity write x²/v² Yo(t zero Zeroth period νπ ω² дх دو دو