The theory of Fourier series and integrals

Author: Philip L. Walker,Peter Leslie Walker

Publisher: John Wiley & Sons Incorporated

ISBN: 9780471901129

Category: Mathematics

Page: 192

View: 6400

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A concise treatment of Fourier series and integrals, with particular emphasis on their relation and importance to science and engineering. Illustrates interesting applications which those with limited mathematical knowledge can execute. Key concepts are supported by examples and exercises at the end of each chapter. Includes background on elementary analysis, a comprehensive bibliography, and a guide to further reading for readers who want to pursue the subject in greater depth.

Introduction to the Theory of Fourier's Series and Integrals

Author: H. S. Carslaw

Publisher: Merchant Books

ISBN: 9781603860680

Category: Mathematics

Page: 336

View: 9915

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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

Author: Norbert Wiener

Publisher: CUP Archive

ISBN: 9780521358842

Category: Mathematics

Page: 201

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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.

Introduction to the Theory of Fourier's Series and Integrals

Author: Horatio Scott Carslaw

Publisher: BiblioBazaar, LLC

ISBN: 9780559202926

Category: History

Page: 336

View: 5979

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This is a pre-1923 historical reproduction that was curated for quality. Quality assurance was conducted on each of these books in an attempt to remove books with imperfections introduced by the digitization process. Though we have made best efforts - the books may have occasional errors that do not impede the reading experience. We believe this work is culturally important and have elected to bring the book back into print as part of our continuing commitment to the preservation of printed works worldwide.

An Introduction to Fourier Series and Integrals

Author: Robert T. Seeley

Publisher: Courier Corporation

ISBN: 0486151794

Category: Mathematics

Page: 112

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DIVThis compact guide emphasizes the relationship between physics and mathematics, introducing Fourier series in the way that Fourier himself used them: as solutions of the heat equation in a disk. 1966 edition. /div

Harmonic Analysis and the Theory of Probability

Author: Salomon Bochner

Publisher: Courier Corporation

ISBN: 0486154807

Category: Mathematics

Page: 192

View: 8824

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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.

Fourier Analysis and Its Applications

Author: G. B. Folland

Publisher: American Mathematical Soc.

ISBN: 9780821847909

Category: Mathematics

Page: 433

View: 384

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This book presents the theory and applications of Fourier series and integrals, eigenfunction expansions, and related topics, on a level suitable for advanced undergraduates. It includes material on Bessel functions, orthogonal polynomials, and Laplace transforms, and it concludes with chapters on generalized functions and Green's functions for ordinary and partial differential equations. The book deals almost exclusively with aspects of these subjects that are useful in physics and engineering, and includes a wide variety of applications. On the theoretical side, it uses ideas from modern analysis to develop the concepts and reasoning behind the techniques without getting bogged down in the technicalities of rigorous proofs.

Analysis II

Differential and Integral Calculus, Fourier Series, Holomorphic Functions

Author: Roger Godement

Publisher: Springer Science & Business Media

ISBN: 3540299262

Category: Mathematics

Page: 448

View: 5267

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Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes. Based on a course given by the author to large audiences at Paris VII University for many years, the exposition proceeds somewhat nonlinearly, blending rigorous mathematics skilfully with didactical and historical considerations. It sets out to illustrate the variety of possible approaches to the main results, in order to initiate the reader to methods, the underlying reasoning, and fundamental ideas. It is suitable for both teaching and self-study. In his familiar, personal style, the author emphasizes ideas over calculations and, avoiding the condensed style frequently found in textbooks, explains these ideas without parsimony of words. The French edition in four volumes, published from 1998, has met with resounding success: the first two volumes are now available in English.

Principles of Fourier Analysis

Author: Kenneth B. Howell

Publisher: CRC Press

ISBN: 1420036904

Category: Mathematics

Page: 792

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Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas. Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author's development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based on the use of Gaussian test functions that yields an even more general -yet simpler -theory than usually presented. Principles of Fourier Analysis stimulates the appreciation and understanding of the fundamental concepts and serves both beginning students who have seen little or no Fourier analysis as well as the more advanced students who need a deeper understanding. Insightful, non-rigorous derivations motivate much of the material, and thought-provoking examples illustrate what can go wrong when formulas are misused. With clear, engaging exposition, readers develop the ability to intelligently handle the more sophisticated mathematics that Fourier analysis ultimately requires.

Real Analysis and Applications

Including Fourier Series and the Calculus of Variations

Author: Frank Morgan

Publisher: American Mathematical Soc.

ISBN: 9780821886113

Category: Mathematics

Page: 197

View: 993

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Real Analysis and Applications starts with a streamlined, but complete, approach to real analysis. It finishes with a wide variety of applications in Fourier series and the calculus of variations, including minimal surfaces, physics, economics, Riemannian geometry, and general relativity. The basic theory includes all the standard topics: limits of sequences, topology, compactness, the Cantor set and fractals, calculus with the Riemann integral, a chapter on the Lebesgue theory, sequences of functions, infinite series, and the exponential and Gamma functions. The applications conclude with a computation of the relativistic precession of Mercury's orbit, which Einstein called "convincing proof of the correctness of the theory [of General Relativity]." The text not only provides clear, logical proofs, but also shows the student how to derive them. The excellent exercises come with select solutions in the back. This is a text that makes it possible to do the full theory and significant applications in one semester. Frank Morgan is the author of six books and over one hundred articles on mathematics. He is an inaugural recipient of the Mathematical Association of America's national Haimo award for excellence in teaching. With this applied version of his Real Analysis text, Morgan brings his famous direct style to the growing numbers of potential mathematics majors who want to see applications along with the theory. The book is suitable for undergraduates interested in real analysis.

Lectures on Measure and Integration

Author: Harold Widom

Publisher: Courier Dover Publications

ISBN: 0486810283

Category: Mathematics

Page: 176

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These well-known and concise lecture notes present the fundamentals of the Lebesgue theory of integration and an introduction to some of the theory's applications. Suitable for advanced undergraduates and graduate students of mathematics, the treatment also covers topics of interest to practicing analysts. Author Harold Widom emphasizes the construction and properties of measures in general and Lebesgue measure in particular as well as the definition of the integral and its main properties. The notes contain chapters on the Lebesgue spaces and their duals, differentiation of measures in Euclidean space, and the application of integration theory to Fourier series.

A Handbook of Fourier Theorems

Author: D. C. Champeney

Publisher: Cambridge University Press

ISBN: 9780521366885

Category: Mathematics

Page: 185

View: 6914

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This handbook presents a collection of the most important theorems in Fourier analysis. Proofs are presented intuitively, without burdensome mathematical rigor, in a form that is accurate but also accessible to a reader who is not a specialized mathematician. This text bridges the gap between books presently on the market by discussing the finer points of the theory. It is self-contained in that it includes examples of the use of the various theorems.

A Panorama of Harmonic Analysis

Author: Steven Krantz

Publisher: Cambridge University Press

ISBN: 9780883850312

Category: Mathematics

Page: 357

View: 7834

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A Panorama of Harmonic Analysis treats the subject of harmonic analysis, from its earliest beginnings to the latest research. Following both an historical and a conceptual genesis, the book discusses Fourier series of one and several variables, the Fourier transform, spherical harmonics, fractional integrals, and singular integrals on Euclidean space. The climax of the book is a consideration of the earlier ideas from the point of view of spaces of homogeneous type. The book culminates with a discussion of wavelets-one of the newest ideas in the subject. A Panorama of Harmonic Analysis is intended for graduate students, advanced undergraduates, mathematicians, and anyone wanting to get a quick overview of the subject of cummutative harmonic analysis. Applications are to mathematical physics, engineering and other parts of hard science. Required background is calculus, set theory, integration theory, and the theory of sequences and series.

Fourier and Laplace Transforms

Author: R. J. Beerends

Publisher: Cambridge University Press

ISBN: 9780521534413

Category: Mathematics

Page: 447

View: 6752

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This textbook presents in a unified manner the fundamentals of both continuous and discrete versions of the Fourier and Laplace transforms. These transforms play an important role in the analysis of all kinds of physical phenomena. As a link between the various applications of these transforms the authors use the theory of signals and systems, as well as the theory of ordinary and partial differential equations. The book is divided into four major parts: periodic functions and Fourier series, non-periodic functions and the Fourier integral, switched-on signals and the Laplace transform, and finally the discrete versions of these transforms, in particular the Discrete Fourier Transform together with its fast implementation, and the z-transform. This textbook is designed for self-study. It includes many worked examples, together with more than 120 exercises, and will be of great value to undergraduates and graduate students in applied mathematics, electrical engineering, physics and computer science.

Integral Transforms and Fourier Series

Author: A. N. Srivastava,Mohammad Ahmad

Publisher: Alpha Science International Limited

ISBN: 9781842656983

Category: Mathematics

Page: 176

View: 9594

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INTEGRAL TRANSFORMS AND FOURIER SERIES presents the fundamentals of Integral Transforms and Fourier Series with their applications in diverse fields including engineering mathematics. Beginning with the basic ideas, concepts, methods and related theorems of Laplace Transforms and their applications the book elegantly deals in detail the theory of Fourier Series along with application of Drichlet's theorem to Fourier Series. The book also covers the basic concepts and techniques in Fourier Transform, Fourier Sine and Fourier Cosine transform of a variety of functions in different types of intervals with applications to boundary value problems are the special features of this section of the book. Apart from basic ideas, properties and applications of Z-Transform, the book prepares the readers for applying Transform Calculus to applicable mathematics by introducing basics of other important transforms such as Mellin, Hilbert, Hankel, Weierstrass and Abel's Transform.