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Titlebook: Introduction to the Theory and Application of the Laplace Transformation; Gustav Doetsch Book 1974 Springer-Verlag Berlin Heidelberg 1974

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书目名称Introduction to the Theory and Application of the Laplace Transformation
编辑Gustav Doetsch
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图书封面Titlebook: Introduction to the Theory and Application of the Laplace Transformation;  Gustav Doetsch Book 1974 Springer-Verlag Berlin Heidelberg 1974
描述In anglo-american 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 on
出版日期Book 1974
关键词Laplace-Transformation; equation; function; proof; theorem
版次1
doihttps://doi.org/10.1007/978-3-642-65690-3
isbn_softcover978-3-642-65692-7
isbn_ebook978-3-642-65690-3
copyrightSpringer-Verlag Berlin Heidelberg 1974
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The Solutions of the Differential Equation for Specific Excitations,combination of functions of the type .; it is easy to survey. Therefore we disregard this part of the problem here, and we presume that .; that is, the system is assumed to be initially at rest. Thus we find the corresponding solution in the image space: . and, consequently, in the original space:
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Book 1974technics, 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, pres
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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 ma
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The Ordinary Differential Equation, specifying Initial Values for Derivatives of Arbitrary Order, a, .′ (0), and .″ (0) were given. Then we would form the higher derivatives, . . (.) and . (.). For . = 0, we would obtain two linear equations in the unknowns .′ (0) and .″ (0). Having solved these equations, we can write the complete solution .(.).
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