Theorie und Anwendung der Laplace-Transformation

ISBN-10: 3642987214

ISBN-13: 9783642987212

Edition: 1937

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Description: st Die Laplacesche Integraltransformation J e- F(t) dt kann als das kontinuierliche Analogon zur Dirichletschen Reihe . :E a"e-}'''s und zur Potenzreihe . :E en z" = . :E c" e-ns betrachtet werden. Wahrend jedoch diese Reihen langst zum Allgemeingut der Mathematiker geh6ren und in den verschiedensten Gebieten angewandt werden, ist die Laplace-Trans­ formation nur einem kleinen Kreis wirklich gelaufig, was urn so be­ dauerlicher ist, als sie an Verwendungsfahigkeit jene Reihen, die sie als Spezialfaile enthalt, noch weit tibertrifft. DaB die Laplace-Transfor­ mation, obwohl sie auf ein viel h6heres Alter als die Dirichletsche Reihe zuriickblicken kann, sich bisher so wenig eingebtirgert hat, liegt in erster Linie daran, daB bisher eine zusammenfassende Darsteilung ihrer Theorie fehlte. Das Material ist tiber die ganze Zeitschriftenliteratur verstreut und oft in andere Untersuchungen eingebettet, wo man es kaum ver­ mutet; vieles steht in alteren Jahrgangen schwer zuganglicher Zeit­ schriften. Dazu kommt, daB manche grundlegende Satze der Theorie zwar den Kennern geHiufig sind, sich aber nirgends explizit formuliert, noch weniger bewiesen finden. Auch das explizit Ausgesprochene und Bewiesene leidet haufig darunter, daB die Beweise unzulanglich oder nicht in wtinschenswertem Umfang gefiihrt sind. Aile diese Umstande lieBen bei der wachsenden Bedeutung der Laplace-Transformation den \iVunsch nach einer Darsteilung immer fiihlbarer werden, die einerseits die theoretischen Grundlagen der Transformation ausfiihrlich und ein­ heitlich zusammenstelit, und andererseits zeigt, in welchen Gebieten sie bisher mit Erfolg angewandt worden ist. Man kann heute innerhalb dessen, was zur Laplace-Transformation zu rechnen ist, drei Richtungen unterscheiden.

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Book details

Copyright year: 1937
Publisher: Springer
Publication date: 1/1/1937
Binding: Paperback
Pages: 438
Size: 6.10" wide x 9.20" long x 0.36" tall
Weight: 1.496

Richard Courant was born in Lublintz, Germany, on January 8, 1888, later becoming an American citizen. He was a mathematician, researcher and teacher, specializing in variational calculus and its applications to physics, computer science, and related fields. He received his Ph.D. from the University of Gottingen, Germany, lectured at Cambridge University and headed the mathematics department at New York University. Courant's writings include Introduction to Calculus and Analysis (1965), written with John Fritz, Differential and Integral Calculus (1965), Methods of Mathematical Physics: Dirichlet's Principle, Conformal Mapping and Minimal Surfaces (1950), and Supersonic Flow and Shock Waves (1948). He edited a mathematics series and contributed to journals and periodicals. Courant received the Distinguished Service Award from the Mathematical Association of America in 1965. He earned the Navy Distinguished Public Service Award, the Knight-Commander's cross, and Germany's Star of the Order of Merit in 1958. Courant died on January 27, 1972.

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