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Laplace-transformaties. --- Z-transformatie. --- Laplace transformation. --- Z transformation.

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Analyse : Fourier analyse --- Laplace transformaties --- Z-transformaties --- Telecommunicatiesystemen --- Systeemanalyse --- Signaalverwerking --- 621.38 --- Linear time invariant system --- Linear time invariant systems --- Signal processing --- System Analysis --- Telecommunication systems

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The Laplace transform is a wonderful tool for solving ordinary and partial differential equations and has enjoyed much success in this realm. With its success, however, a certain casualness has been bred concerning its application, without much regard for hypotheses and when they are valid. Even proofs of theorems often lack rigor, and dubious mathematical practices are not uncommon in the literature for students. In the present text, I have tried to bring to the subject a certain amount of mathematical correctness and make it accessible to un­ dergraduates. Th this end, this text addresses a number of issues that are rarely considered. For instance, when we apply the Laplace trans­ form method to a linear ordinary differential equation with constant coefficients, any(n) + an-lY(n-l) + · · · + aoy = f(t), why is it justified to take the Laplace transform of both sides of the equation (Theorem A. 6)? Or, in many proofs it is required to take the limit inside an integral. This is always fraught with danger, especially with an improper integral, and not always justified. I have given complete details (sometimes in the Appendix) whenever this procedure is required. IX X Preface Furthermore, it is sometimes desirable to take the Laplace trans­ form of an infinite series term by term. Again it is shown that this cannot always be done, and specific sufficient conditions are established to justify this operation.

Laplace transformation. --- Laplace transformaties --- 519.6 --- Laplace transformation --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Analysis. --- Global analysis (Mathematics). --- Transformation, Laplace --- Calculus, Operational --- Differential equations --- Transformations (Mathematics) --- 517.1 Mathematical analysis --- Mathematical analysis

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Mathematical analysis --- 517 --- Analyse (wiskunde) --- Laplace --- Maximum --- Minimum --- Reeksen --- Vectoranalyse --- Wiskunde --- differentiaalvergelijkingen --- 167 --- Analyse : Fourier analyse --- Analyse : Fourier transformaties --- Analyse : Laplace transformaties --- Analyse : afgeleiden --- Analyse : differentialen --- Analyse : integralen --- Analyse : rechten --- Analyse : rijen --- Wiskunde : probleemoplossend denken --- calculus --- Calculus --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Functions --- Geometry, Infinitesimal --- 517 Analysis --- Analysis --- #WBIB:dd.Lic.L.De Busschere --- 51(076.1) --- Laplacetransformatie --- analyse --- complexe variabelen --- differentialen --- fourieranalyse --- fourierreeksen --- integralen --- maxima wiskunde --- meetkunde --- minima --- oefeningen --- oneindige reeksen --- oppervlakteintegralen --- partiële afgeleiden --- reeksen --- vectorruimten --- wiskunde --- Mathematics --- Problems, exercises, etc. --- Wiskundige analyse : vraagstukken. --- Calcul différentiel --- Calcul intégral --- Advanced calculus --- Exercices