An Introduction To Fourier Series And Integrals

Author : Robert T. Seeley
Publisher : Courier Corporation
Page : 116 pages
File Size : 48,6 Mb
Release : 2014-02-20
Category : Mathematics
ISBN : 9780486151793

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An Introduction to Fourier Series and Integrals by Robert T. Seeley Pdf

A compact, sophomore-to-senior-level guide, Dr. Seeley's text introduces Fourier series in the way that Joseph Fourier himself used them: as solutions of the heat equation in a disk. Emphasizing the relationship between physics and mathematics, Dr. Seeley focuses on results of greatest significance to modern readers. Starting with a physical problem, Dr. Seeley sets up and analyzes the mathematical modes, establishes the principal properties, and then proceeds to apply these results and methods to new situations. The chapter on Fourier transforms derives analogs of the results obtained for Fourier series, which the author applies to the analysis of a problem of heat conduction. Numerous computational and theoretical problems appear throughout the text.

Author : Horatio Scott Carslaw
Publisher : Legare Street Press
Page : 0 pages
File Size : 44,5 Mb
Release : 2022-10-27
Category : History
ISBN : 1015773303

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Introduction to the Theory of Fourier's Series and Integrals by Horatio Scott Carslaw Pdf

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Author : Howard J. Wilcox,David L. Myers
Publisher : Courier Corporation
Page : 194 pages
File Size : 46,9 Mb
Release : 2012-04-30
Category : Mathematics
ISBN : 9780486137476

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An Introduction to Lebesgue Integration and Fourier Series by Howard J. Wilcox,David L. Myers Pdf

This book arose out of the authors' desire to present Lebesgue integration and Fourier series on an undergraduate level, since most undergraduate texts do not cover this material or do so in a cursory way. The result is a clear, concise, well-organized introduction to such topics as the Riemann integral, measurable sets, properties of measurable sets, measurable functions, the Lebesgue integral, convergence and the Lebesgue integral, pointwise convergence of Fourier series and other subjects. The authors not only cover these topics in a useful and thorough way, they have taken pains to motivate the student by keeping the goals of the theory always in sight, justifying each step of the development in terms of those goals. In addition, whenever possible, new concepts are related to concepts already in the student's repertoire. Finally, to enable readers to test their grasp of the material, the text is supplemented by numerous examples and exercises. Mathematics students as well as students of engineering and science will find here a superb treatment, carefully thought out and well presented , that is ideal for a one semester course. The only prerequisite is a basic knowledge of advanced calculus, including the notions of compactness, continuity, uniform convergence and Riemann integration.

Author : H. S. CARSLAW
Publisher : Unknown
Page : 0 pages
File Size : 53,7 Mb
Release : 2018
Category : Electronic
ISBN : 1033507733

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INTRODUCTION TO THE THEORY OF FOURIER'S SERIES AND INTEGRALS by H. S. CARSLAW Pdf

Author : Horatio Scott Carslaw
Publisher : Unknown
Page : 440 pages
File Size : 51,6 Mb
Release : 1930
Category : Definite integrals
ISBN : UCSD:31822014010458

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Introduction to the Theory of Fourier's Series and Integrals by Horatio Scott Carslaw Pdf

Author : Elias M. Stein,Rami Shakarchi
Publisher : Princeton University Press
Page : 326 pages
File Size : 52,8 Mb
Release : 2011-02-11
Category : Mathematics
ISBN : 9781400831234

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Fourier Analysis by Elias M. Stein,Rami Shakarchi Pdf

This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions. The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression. In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

Author : Edward Charles Titchmarsh
Publisher : Unknown
Page : 412 pages
File Size : 54,6 Mb
Release : 1967
Category : Fourier series
ISBN : UOM:49015000688060

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Introduction to the Theory of Fourier Integrals by Edward Charles Titchmarsh Pdf

Author : Allan Pinkus,Samy Zafrany
Publisher : Cambridge University Press
Page : 204 pages
File Size : 53,8 Mb
Release : 1997-07-10
Category : Mathematics
ISBN : 0521597714

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Fourier Series and Integral Transforms by Allan Pinkus,Samy Zafrany Pdf

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

Author : Peter L. Walker
Publisher : Unknown
Page : 208 pages
File Size : 42,9 Mb
Release : 1986-06-03
Category : Mathematics
ISBN : UOM:39015015628418

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The Theory of Fourier Series and Integrals by Peter L. Walker Pdf

In this book, the author has drawn on his considerable experience of teaching analysis to give a concise explanation of the theory of Fourier series and integrals.

Author : H. S. Carslaw
Publisher : Forgotten Books
Page : 340 pages
File Size : 45,7 Mb
Release : 2017-10-15
Category : Mathematics
ISBN : 0265332206

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Introduction to the Theory of Fourier's Series and Integrals (Classic Reprint) by H. S. Carslaw Pdf

Excerpt from Introduction to the Theory of Fourier's Series and Integrals The modern theory of integration, associated chiefly with the name of Lebesgue, has introduced into the Theory of Fourier's Series and Integrals functions of a far more complicated nature. Various writers, notably W. H. Young, are engaged in building up a theory of these and allied series much more advanced than any thing treated in this book. These developments are in the meantime chiefly interesting to the Pure Mathematician specialising in the Theory of Functions of a Real Variable. My purpose has been to remove some of the difficulties of the Applied Mathematician. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Author : Horatio Scott CARSLAW
Publisher : Unknown
Page : 0 pages
File Size : 41,6 Mb
Release : 1921
Category : Electronic
ISBN : OCLC:559366166

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Introduction to the Theory of Fourier's Series and Integrals ... Second Edition, Completely Revised by Horatio Scott CARSLAW Pdf

Author : H. Dym,H. P. McKean
Publisher : Academic Press
Page : 316 pages
File Size : 40,8 Mb
Release : 1985-10-28
Category : Mathematics
ISBN : UCSD:31822016450041

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Fourier Series and Integrals by H. Dym,H. P. McKean Pdf

The ideas of Fourier have made their way into every branch of mathematics and mathematical physics, from the theory of numbers to quantum mechanics. Fourier Series and Integrals focuses on the extraordinary power and flexibility of Fourier's basic series and integrals and on the astonishing variety of applications in which it is the chief tool. It presents a mathematical account of Fourier ideas on the circle and the line, on finite commutative groups, and on a few important noncommutative groups. A wide variety of exercises are placed in nearly every section as an integral part of the text.

Author : Christopher Donald Sogge
Publisher : Cambridge University Press
Page : 250 pages
File Size : 45,7 Mb
Release : 1993-02-26
Category : Mathematics
ISBN : 9780521434645

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Fourier Integrals in Classical Analysis by Christopher Donald Sogge Pdf

An advanced monograph concerned with modern treatments of central problems in harmonic analysis.

Author : H. S. Carslaw
Publisher : Unknown
Page : 342 pages
File Size : 43,5 Mb
Release : 2011-09
Category : Mathematics
ISBN : 1418166944

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Introduction to the Theory of Fourier's Series and Integrals, by H.S. Carslaw. by H. S. Carslaw Pdf

Author : Javier Duoandikoetxea Zuazo
Publisher : American Mathematical Soc.
Page : 248 pages
File Size : 53,9 Mb
Release : 2001-01-01
Category : Mathematics
ISBN : 0821883844

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Fourier Analysis by Javier Duoandikoetxea Zuazo Pdf

Fourier analysis encompasses a variety of perspectives and techniques. This volume presents the real variable methods of Fourier analysis introduced by Calderón and Zygmund. The text was born from a graduate course taught at the Universidad Autonoma de Madrid and incorporates lecture notes from a course taught by José Luis Rubio de Francia at the same university. Motivated by the study of Fourier series and integrals, classical topics are introduced, such as the Hardy-Littlewood maximal function and the Hilbert transform. The remaining portions of the text are devoted to the study of singular integral operators and multipliers. Both classical aspects of the theory and more recent developments, such as weighted inequalities, H1, BMO spaces, and the T1 theorem, are discussed. Chapter 1 presents a review of Fourier series and integrals; Chapters 2 and 3 introduce two operators that are basic to the field: the Hardy-Littlewood maximal function and the Hilbert transform in higher dimensions. Chapters 4 and 5 discuss singular integrals, including modern generalizations. Chapter 6 studies the relationship between H1, BMO, and singular integrals; Chapter 7 presents the elementary theory of weighted norm inequalities. Chapter 8 discusses Littlewood-Paley theory, which had developments that resulted in a number of applications. The final chapter concludes with an important result, the T1 theorem, which has been of crucial importance in the field. This volume has been updated and translated from the original Spanish edition (1995). Minor changes have been made to the core of the book; however, the sections, "Notes and Further Results" have been considerably expanded and incorporate new topics, results, and references. It is geared toward graduate students seeking a concise introduction to the main aspects of the classical theory of singular operators and multipliers. Prerequisites include basic knowledge in Lebesgue integrals and functional analysis.