Tables of Laplace Transforms, F. Oberhettinger; L. Badii

Автор: Dyke Phil
Название: Introduction to Laplace Transforms and Fourier Series
ISBN: 144716394X ISBN-13(EAN): 9781447163947
Издательство: Springer
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Описание: This advanced undergraduate/graduate textbook provides an easy-to-read account of Fourier series, wavelets and Laplace transforms. It features many worked examples with all solutions provided.

Автор: Urs Graf
Название: Applied Laplace Transforms and z-Transforms for Scientists and Engineers
ISBN: 3034895933 ISBN-13(EAN): 9783034895934
Издательство: Springer
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Описание: The theory of Laplace transformation is an important part of the mathematical background required for engineers, physicists and mathematicians. The code is placed in front of the already built-in code of Laplace and z-transformations of Mathematica so that built-in functions not covered by the Package remain available.

Автор: Wolfgang Arendt; Charles J.K. Batty; Matthias Hieb
Название: Vector-valued Laplace Transforms and Cauchy Problems
ISBN: 3034803273 ISBN-13(EAN): 9783034803274
Издательство: Springer
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Описание: In addition to systematic coverage of vector-valued Laplace transform theory, ranging from representation to Tauberian theorems, this second edition develops the theory of linear Cauchy problems and semigroups of operators and introduces the Bochner integral.

Автор: F. Oberhettinger
Название: Tables of Bessel Transforms
ISBN: 3540059970 ISBN-13(EAN): 9783540059974
Издательство: Springer
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Описание: This material represents a collection of integral tra- forms involving Bessel (or related) functions as kernel. The following types of inversion formulas have been singled out. k I. g(y) = f (x) (xy) 2J (xy) dx J V 0 k I' . f (x) g (y) (xy) 2J (xy) dy J V 0 II. g(y) f(x) (XY) K (xy)dx J v 0 c]ioo k 1 II'. f (x) = g (y) (xy) 2 Iv (xy) ] I_v(xy)]dy J 27fT c-ioo or also c+ioo k 1 II." f(x) = g (y) (xy) 2Iv (xy) dx J rri oo c-i k III. g(y) f(x) (xy) 2y (xy) dx + J v 0 k III' . f(x) g(y) (xy) "1lv (xy) dy J 0 k IV. g(y) f (x) (xy) "Kv (xy) dx J 0 k g(y) (xy) 2Y (xy)dy IV' - f(x) J v 0 V Preface V. g(y) f(X)Kix(y)dx J 0 -2 -1 sinh (7TX) V'. f(x) 27T x g(y)y Kix(y)dy J 0 21- r( ] - v)r( + + v)]-1 VI. g(y) . J f (x) (xy) s (xy) dx o, v l- -1 VI' . f(x) 2 r ( ] - v) r ( + + v) ] - - J -5 (xy)]dy g(y) (XY) S, v(xy), v 0 xy) ]dX VII. g(y) f(x)\ J 0 0 VII' - f(x) g(y) \ (xy) lz]dy f 0 0 with \ (z) o (For notations and definitions see the appendix of this book. ) The transform VII is also known as the divisor transform.

Автор: F. Oberhettinger
Название: Tables of Mellin Transforms
ISBN: 3540069429 ISBN-13(EAN): 9783540069423
Издательство: Springer
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Описание: This is partially due to the fact that if c(z) corresponding to a given q,(x) by (a) is known, then c(z) belonging to xaq,(x) or more general to P xaq,(x ) (p real) is likewise known. ) A list of major contributions conce~ning Mellin trans- forms is added at the end of the introduction. * . * * * . * . * * * * . * . * . * * * . * . * .

Автор: Dyke, P. P. G.
Название: An Introduction to Laplace transforms and Fourier series
ISBN: 1852330155 ISBN-13(EAN): 9781852330156
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Описание: This introduction to Laplace transforms and Fourier series is aimed at second year students in applied mathematics. Mathematics students do not usually meet this material until later in their degree course but applied mathematicians and engineers need an early introduction.

Автор: Fritz Oberhettinger
Название: Tables of Fourier Transforms and Fourier Transforms of Distributions
ISBN: 3540506306 ISBN-13(EAN): 9783540506300
Издательство: Springer
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Описание: These tables represent a new, revised and enlarged version of the previously published book by this author, entitled "Tabellen zur Fourier Transformation" (Springer Verlag 1957). Known errors have been correc- ted, apart from the addition of a considerable number of new results, which involve almost exclusively higher functions. Again, the follow- ing tables contain a collection of integrals of the form J f(x)cos(xy)dx Fourier Cosine Transform (Al o (B) J f(x)sin(xy)dx Fourier Sine Transform o (C) ge(y) = J f(x)eixYdx Exponential Fourier Transform -00 Clearly, (A) and (B) are special cases of (C) if f(x) is respec- tively an even or an odd function. The transform parameter y in (A) and (B) is assumed to be positive, while in (C) negative values are also included. A possible analytic continuation to complex parameters y* should present no difficulties. In some cases the result function g(y) is given over a partial range of y only. This means that g(y) for the remaining part of y cannot be given in a reasonably simple form. Under certain conditions the following inversion formulas for (A), (B), (C) hold: (A' ) f(x) = 2 J g (y)cos(xy)dy 11 0 c 2 J (B') f (x) gs(y)sin(xy)dy 11 0 -1 00 -ix (C' ) f(x) = (211) J ge(y)e Ydy In the following parts I, II, III tables for the transforms (A), (B) and (C) are given.