Integral transforms and their applications / Brian Davies.

By:

Davies, B. (Brian), 1937-

Material type: Text

TextSeries: Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 25.Publication details: New York : Springer, 2002.Edition: 3rd edDescription: 367 p. : illISBN:

0387953140 (alk. paper)

Subject(s):

Integral transforms

DDC classification:

515.723 DAV

LOC classification:

QA1 .A647 vol. 25, 2001 QA432

Contents:

Functions of a Complex Variable Brian Davies Pages 1-26 The Laplace Transform Brian Davies Pages 27-38 The Inversion Integral Brian Davies Pages 39-56 Ordinary Differential Equations Brian Davies Pages 57-84 Partial Differential Equations I Brian Davies Pages 85-96 Integral Equations Brian Davies Pages 97-109 The Fourier Transform Brian Davies Pages 111-128 Partial Differential Equations II Brian Davies Pages 129-142 Generalized Functions Brian Davies Pages 143-162 Green’s Functions Brian Davies Pages 163-179 Transforms in Several Variables Brian Davies Pages 181-194 The Mellin Transform Brian Davies Pages 195-210 Application to Sums and Integrals Brian Davies Pages 211-226 Hankel Transforms Brian Davies Pages 227-248 Integral Transforms Generated by Green’s Functions Brian Davies Pages 249-264 The Wiener-Hopf Technique Brian Davies Pages 265-281 Methods Based on Cauchy Integrals Brian Davies Pages 283-302 Laplace’s Method for Ordinary Differential Equations Brian Davies Pages 303-326 Numerical Inversion of Laplace Transforms Brian Davies Pages 327-355 Back Matter Pages 357-369

Summary: Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in re search and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numeri cal and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathe matical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs. Pasadena, California J.E. Marsden Providence, Rhode Island L. Sirovich Houston, Texas M. Golubitsky College Park, Maryland S.S. Antman Preface to the Third Edition It is more than 25 years since I finished the manuscript of the first edition of this volume, and it is indeed gratifying that the book has been in use over such a long period and that the publishers have requested a third edition.

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Holdings
Item type	Current library	Call number	Status	Date due	Barcode
Project book	CUTN Central Library Sciences	515.723 DAV (Browse shelf(Opens below))	Checked out to Renuka Devi V (20019T)	31/01/2024	48836

"TAM will publish ... will complement the Applied Mathematical Sciences (AMS) series ..." -- Pref.

Includes bibliographical references and index.

Functions of a Complex Variable
Brian Davies
Pages 1-26
The Laplace Transform
Brian Davies
Pages 27-38
The Inversion Integral
Brian Davies
Pages 39-56
Ordinary Differential Equations
Brian Davies
Pages 57-84
Partial Differential Equations I
Brian Davies
Pages 85-96
Integral Equations
Brian Davies
Pages 97-109
The Fourier Transform
Brian Davies
Pages 111-128
Partial Differential Equations II
Brian Davies
Pages 129-142
Generalized Functions
Brian Davies
Pages 143-162
Green’s Functions
Brian Davies
Pages 163-179
Transforms in Several Variables
Brian Davies
Pages 181-194
The Mellin Transform
Brian Davies
Pages 195-210
Application to Sums and Integrals
Brian Davies
Pages 211-226
Hankel Transforms
Brian Davies
Pages 227-248
Integral Transforms Generated by Green’s Functions
Brian Davies
Pages 249-264
The Wiener-Hopf Technique
Brian Davies
Pages 265-281
Methods Based on Cauchy Integrals
Brian Davies
Pages 283-302
Laplace’s Method for Ordinary Differential Equations
Brian Davies
Pages 303-326
Numerical Inversion of Laplace Transforms
Brian Davies
Pages 327-355
Back Matter
Pages 357-369

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in re search and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numeri cal and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathe matical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs. Pasadena, California J.E. Marsden Providence, Rhode Island L. Sirovich Houston, Texas M. Golubitsky College Park, Maryland S.S. Antman Preface to the Third Edition It is more than 25 years since I finished the manuscript of the first edition of this volume, and it is indeed gratifying that the book has been in use over such a long period and that the publishers have requested a third edition.

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