Introduction to the Theory of Fourier's Series and Integrals

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Author: H. S. Carslaw

Publisher: Merchant Books

ISBN: 9781603860680

Category: Mathematics

Page: 336

View: 5366

An Unabridged Printing Of The Revised, Second Edition: Rational And Irrational Numbers - Infinite Sequences And Series - Functions Of A Single Variable; Limits And Continuity - The Definite Integral - The Theory Of Infinite Series Whose Terms Are Functions Of A Single Variable- Definite Integrals Containing An Arbitrary Parameter - Fourier's Series - The Nature Of The Convergence Of Fourier's Series - The Approximation Curves And Gibbs Phenomenon In Fourier's Series - Fourier's Integrals - Examples - Appendix - General Index

The Fourier Integral and Certain of Its Applications

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Author: Norbert Wiener

Publisher: CUP Archive

ISBN: 9780521358842

Category: Mathematics

Page: 201

View: 385

The book was written from lectures given at the University of Cambridge and maintains throughout a high level of rigour whilst remaining a highly readable and lucid account. Topics covered include the Planchard theory of the existence of Fourier transforms of a function of L2 and Tauberian theorems. The influence of G. H. Hardy is apparent from the presence of an application of the theory to the prime number theorems of Hadamard and de la Vallee Poussin. Both pure and applied mathematicians will welcome the reissue of this classic work. For this reissue, Professor Kahane's Foreword briefly describes the genesis of Wiener's work and its later significance to harmonic analysis and Brownian motion.

Fourier Series and Integral Transforms

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Author: Allan Pinkus,Samy Zafrany

Publisher: Cambridge University Press

ISBN: 9780521597715

Category: Mathematics

Page: 189

View: 4620

Textbook covering the basics of Fourier series, Fourier transforms and Laplace transforms.

Integral Transforms and Their Applications, Third Edition

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Author: Lokenath Debnath,Dambaru Bhatta

Publisher: CRC Press

ISBN: 1482223570

Category: Mathematics

Page: 818

View: 3270

Integral Transforms and Their Applications, Third Edition covers advanced mathematical methods for many applications in science and engineering. The book is suitable as a textbook for senior undergraduate and first-year graduate students and as a reference for professionals in mathematics, engineering, and applied sciences. It presents a systematic development of the underlying theory as well as a modern approach to Fourier, Laplace, Hankel, Mellin, Radon, Gabor, wavelet, and Z transforms and their applications. New to the Third Edition New material on the historical development of classical and modern integral transforms New sections on Fourier transforms of generalized functions, the Poisson summation formula, the Gibbs phenomenon, and the Heisenberg uncertainty principle Revised material on Laplace transforms and double Laplace transforms and their applications New examples of applications in mechanical vibrations, electrical networks, quantum mechanics, integral and functional equations, fluid mechanics, mathematical statistics, special functions, and more New figures that facilitate a clear understanding of physical explanations Updated exercises with solutions, tables of integral transforms, and bibliography Through numerous examples and end-of-chapter exercises, this book develops readers’ analytical and computational skills in the theory and applications of transform methods. It provides accessible working knowledge of the analytical methods and proofs required in pure and applied mathematics, physics, and engineering, preparing readers for subsequent advanced courses and research in these areas.

Integral Transforms and Their Applications, Second Edition

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Author: Lokenath Debnath,Dambaru Bhatta

Publisher: CRC Press

ISBN: 9781584885757

Category: Mathematics

Page: 722

View: 7102

Keeping the style, content, and focus that made the first edition a bestseller, Integral Transforms and their Applications, Second Edition stresses the development of analytical skills rather than the importance of more abstract formulation. The authors provide a working knowledge of the analytical methods required in pure and applied mathematics, physics, and engineering. The second edition includes many new applications, exercises, comments, and observations with some sections entirely rewritten. It contains more than 500 worked examples and exercises with answers as well as hints to selected exercises. The most significant changes in the second edition include: New chapters on fractional calculus and its applications to ordinary and partial differential equations, wavelets and wavelet transformations, and Radon transform Revised chapter on Fourier transforms, including new sections on Fourier transforms of generalized functions, Poissons summation formula, Gibbs phenomenon, and Heisenbergs uncertainty principle A wide variety of applications has been selected from areas of ordinary and partial differential equations, integral equations, fluid mechanics and elasticity, mathematical statistics, fractional ordinary and partial differential equations, and special functions A broad spectrum of exercises at the end of each chapter further develops analytical skills in the theory and applications of transform methods and a deeper insight into the subject A systematic mathematical treatment of the theory and method of integral transforms, the book provides a clear understanding of the subject and its varied applications in mathematics, applied mathematics, physical sciences, and engineering.

Harmonic Analysis and the Theory of Probability

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Author: Salomon Bochner

Publisher: Courier Corporation

ISBN: 0486154807

Category: Mathematics

Page: 192

View: 5687

Written by a distinguished mathematician and educator, this classic text emphasizes stochastic processes and the interchange of stimuli between probability and analysis. It also introduces the author's innovative concept of the characteristic functional. 1955 edition.

Handbook of Mathematical Formulas and Integrals

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Author: Alan Jeffrey,Hui Hui Dai

Publisher: Elsevier

ISBN: 9780080556840

Category: Mathematics

Page: 592

View: 2074

The extensive additions, and the inclusion of a new chapter, has made this classic work by Jeffrey, now joined by co-author Dr. H.H. Dai, an even more essential reference for researchers and students in applied mathematics, engineering, and physics. It provides quick access to important formulas, relationships between functions, and mathematical techniques that range from matrix theory and integrals of commonly occurring functions to vector calculus, ordinary and partial differential equations, special functions, Fourier series, orthogonal polynomials, and Laplace and Fourier transforms. During the preparation of this edition full advantage was taken of the recently updated seventh edition of Gradshteyn and Ryzhik’s Table of Integrals, Series, and Products and other important reference works. Suggestions from users of the third edition of the Handbook have resulted in the expansion of many sections, and because of the relevance to boundary value problems for the Laplace equation in the plane, a new chapter on conformal mapping, has been added, complete with an atlas of useful mappings. Comprehensive coverage in reference form of the branches of mathematics used in science and engineering Organized to make results involving integrals and functions easy to locate Results illustrated by worked examples

Nonlinear Integral Operators and Applications

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Author: Carlo Bardaro,Julian Musielak,Gianluca Vinti

Publisher: Walter de Gruyter

ISBN: 9783110175516

Category: Mathematics

Page: 201

View: 4242

This volume presents a comprehensive treatment of approximation theory by means of nonlinear integral operator in function spaces. In particular, the fundamental notions of approximate identity for kernels of nonlinear operators and a general concept of modulus of continuity are developed.