Introduction to the Theory and Application of the Laplace Transformation
Authors: Doetsch, G.
Editors: Nader, W. (Ed.)
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In angloamerican literature there exist numerous books, devoted to the application of the Laplace transformation in technical domains such as electrotechnics, mechanics etc. Chiefly, they treat problems which, in mathematical language, are governed by ordi nary and partial differential equations, in various physically dressed forms. The theoretical foundations of the Laplace transformation are presented usually only in a simplified manner, presuming special properties with respect to the transformed func tions, which allow easy proofs. By contrast, the present book intends principally to develop those parts of the theory of the Laplace transformation, which are needed by mathematicians, physicists a,nd engineers in their daily routine work, but in complete generality and with detailed, exact proofs. The applications to other mathematical domains and to technical prob lems are inserted, when the theory is adequately· developed to present the tools necessary for their treatment. Since the book proceeds, not in a rigorously systematic manner, but rather from easier to more difficult topics, it is suited to be read from the beginning as a textbook, when one wishes to familiarize oneself for the first time with the Laplace transforma tion. For those who are interested only in particular details, all results are specified in "Theorems" with explicitly formulated assumptions and assertions. Chapters 114 treat the question of convergence and the mapping properties of the Laplace transformation. The interpretation of the transformation as the mapping of one function space to another (original and image functions) constitutes the dom inating idea of all subsequent considerations.
 Table of contents (40 chapters)


Introduction of the Laplace Integral from Physical and Mathematical Points of View
Pages 16

Examples of Laplace Integrals. Precise Definition of Integration
Pages 713

The HalfPlane of Convergence
Pages 1318

The Laplace Integral as a Transformation
Pages 1920

The Unique Inverse of the Laplace Transformation
Pages 2025

Table of contents (40 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Introduction to the Theory and Application of the Laplace Transformation
 Authors

 G. Doetsch
 Editors

 W. Nader
 Translated by
 Nader, W.
 Copyright
 1974
 Publisher
 SpringerVerlag Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 eBook ISBN
 9783642656903
 DOI
 10.1007/9783642656903
 Softcover ISBN
 9783642656927
 Edition Number
 1
 Number of Pages
 VIII, 327
 Topics