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An Introduction To Fourier Series And Integrals
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Book Synopsis An Introduction to Fourier Series and Integrals by : Robert T. Seeley
Download or read book An Introduction to Fourier Series and Integrals written by Robert T. Seeley and published by Courier Corporation. This book was released on 2014-02-20 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Lebesgue Integration and Fourier Series by : Howard J. Wilcox
Download or read book An Introduction to Lebesgue Integration and Fourier Series written by Howard J. Wilcox and published by Courier Corporation. This book was released on 2012-04-30 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to the Theory of Fourier's Series and Integrals by : Horatio Scott Carslaw
Download or read book Introduction to the Theory of Fourier's Series and Integrals written by Horatio Scott Carslaw and published by Legare Street Press. This book was released on 2022-10-27 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fourier Analysis by : Elias M. Stein
Download or read book Fourier Analysis written by Elias M. Stein and published by Princeton University Press. This book was released on 2011-02-11 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to the Theory of Fourier's Series and Integrals by : Horatio Scott Carslaw
Download or read book Introduction to the Theory of Fourier's Series and Integrals written by Horatio Scott Carslaw and published by . This book was released on 1930 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to the Theory of Fourier's Series and Integrals by : H. S. Carslaw
Download or read book Introduction to the Theory of Fourier's Series and Integrals written by H. S. Carslaw and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fourier Analysis by : Javier Duoandikoetxea Zuazo
Download or read book Fourier Analysis written by Javier Duoandikoetxea Zuazo and published by American Mathematical Soc.. This book was released on 2001-01-01 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to the Theory of Fourier's Series and Integrals by : Horatio Scott Carslaw
Download or read book Introduction to the Theory of Fourier's Series and Integrals written by Horatio Scott Carslaw and published by . This book was released on 1921 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fourier Integrals in Classical Analysis by : Christopher Donald Sogge
Download or read book Fourier Integrals in Classical Analysis written by Christopher Donald Sogge and published by Cambridge University Press. This book was released on 1993-02-26 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: An advanced monograph concerned with modern treatments of central problems in harmonic analysis.
Book Synopsis The Fourier Integral and Certain of Its Applications by : Norbert Wiener
Download or read book The Fourier Integral and Certain of Its Applications written by Norbert Wiener and published by CUP Archive. This book was released on 1988-11-17 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Fourier Analysis and Generalised Functions by : Sir M J Lighthill
Download or read book Introduction to Fourier Analysis and Generalised Functions written by Sir M J Lighthill and published by Hassell Street Press. This book was released on 2021-09-09 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Book Synopsis Introduction to the Theory of Fourier's Series and Integrals ... Second Edition, Completely Revised by : Horatio Scott CARSLAW
Download or read book Introduction to the Theory of Fourier's Series and Integrals ... Second Edition, Completely Revised written by Horatio Scott CARSLAW and published by . This book was released on 1921 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Table of Integrals, Series, and Products by : I. S. Gradshteyn
Download or read book Table of Integrals, Series, and Products written by I. S. Gradshteyn and published by Academic Press. This book was released on 2014-05-10 with total page 1206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of Integrals, Series, and Products provides information pertinent to the fundamental aspects of integrals, series, and products. This book provides a comprehensive table of integrals. Organized into 17 chapters, this book begins with an overview of elementary functions and discusses the power of binomials, the exponential function, the logarithm, the hyperbolic function, and the inverse trigonometric function. This text then presents some basic results on vector operators and coordinate systems that are likely to be useful during the formulation of many problems. Other chapters consider inequalities that range from basic algebraic and functional inequalities to integral inequalities and fundamental oscillation and comparison theorems for ordinary differential equations. This book discusses as well the important part played by integral transforms. The final chapter deals with Fourier and Laplace transforms that provides so much information about other integrals. This book is a valuable resource for mathematicians, engineers, scientists, and research workers.
Book Synopsis Introduction to the Theory of Fourier's Series and Integrals and the Mathematical Theory of the Conduction of Heat by : Horatio Scott Carslaw
Download or read book Introduction to the Theory of Fourier's Series and Integrals and the Mathematical Theory of the Conduction of Heat written by Horatio Scott Carslaw and published by . This book was released on 1906 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fourier Integral Operators by : J.J. Duistermaat
Download or read book Fourier Integral Operators written by J.J. Duistermaat and published by Springer Science & Business Media. This book was released on 2010-11-03 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a useful introduction to the subject of Fourier Integral Operators and is based on the author’s classic set of notes. Covering a range of topics from Hörmander’s exposition of the theory, Duistermaat approaches the subject from symplectic geometry and includes application to hyperbolic equations (= equations of wave type) and oscillatory asymptotic solutions which may have caustics. This text is suitable for mathematicians and (theoretical) physicists with an interest in (linear) partial differential equations, especially in wave propagation, rep. WKB-methods.
Book Synopsis Fourier Analysis and Approximation of Functions by : Roald M. Trigub
Download or read book Fourier Analysis and Approximation of Functions written by Roald M. Trigub and published by Springer Science & Business Media. This book was released on 2004-09-07 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Fourier Analysis and Approximation of Functions basics of classical Fourier Analysis are given as well as those of approximation by polynomials, splines and entire functions of exponential type. In Chapter 1 which has an introductory nature, theorems on convergence, in that or another sense, of integral operators are given. In Chapter 2 basic properties of simple and multiple Fourier series are discussed, while in Chapter 3 those of Fourier integrals are studied. The first three chapters as well as partially Chapter 4 and classical Wiener, Bochner, Bernstein, Khintchin, and Beurling theorems in Chapter 6 might be interesting and available to all familiar with fundamentals of integration theory and elements of Complex Analysis and Operator Theory. Applied mathematicians interested in harmonic analysis and/or numerical methods based on ideas of Approximation Theory are among them. In Chapters 6-11 very recent results are sometimes given in certain directions. Many of these results have never appeared as a book or certain consistent part of a book and can be found only in periodics; looking for them in numerous journals might be quite onerous, thus this book may work as a reference source. The methods used in the book are those of classical analysis, Fourier Analysis in finite-dimensional Euclidean space Diophantine Analysis, and random choice.
Book Synopsis Introduction to the Theory of Fourier Integrals by : Edward Charles Titchmarsh
Download or read book Introduction to the Theory of Fourier Integrals written by Edward Charles Titchmarsh and published by . This book was released on 1967 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:
