Fourier Series

Author : Rajendra Bhatia
Publisher : MAA
Page : 134 pages
File Size : 47,9 Mb
Release : 2005-03-03
Category : Mathematics
ISBN : 0883857405

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Fourier Series by Rajendra Bhatia Pdf

This is a concise introduction to Fourier series covering history, major themes, theorems, examples, and applications. It can be used for self study, or to supplement undergraduate courses on mathematical analysis. Beginning with a brief summary of the rich history of the subject over three centuries, the reader will appreciate how a mathematical theory develops in stages from a practical problem (such as conduction of heat) to an abstract theory dealing with concepts such as sets, functions, infinity, and convergence. The abstract theory then provides unforeseen applications in diverse areas. Exercises of varying difficulty are included throughout to test understanding. A broad range of applications are also covered, and directions for further reading and research are provided, along with a chapter that provides material at a more advanced level suitable for graduate students.

Author : Ronald Newbold Bracewell
Publisher : Unknown
Page : 128 pages
File Size : 46,7 Mb
Release : 1978
Category : Fourier transformations
ISBN : OCLC:220097501

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The Fourier Transform and Its Applications by Ronald Newbold Bracewell Pdf

Author : Robert T. Seeley
Publisher : Courier Corporation
Page : 116 pages
File Size : 55,6 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 : Georgi P. Tolstov
Publisher : Courier Corporation
Page : 354 pages
File Size : 51,7 Mb
Release : 2012-03-14
Category : Mathematics
ISBN : 9780486141749

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Fourier Series by Georgi P. Tolstov Pdf

This reputable translation covers trigonometric Fourier series, orthogonal systems, double Fourier series, Bessel functions, the Eigenfunction method and its applications to mathematical physics, operations on Fourier series, and more. Over 100 problems. 1962 edition.

Author : Juan Arias de Reyna
Publisher : Springer
Page : 179 pages
File Size : 46,7 Mb
Release : 2004-10-14
Category : Mathematics
ISBN : 9783540458227

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Pointwise Convergence of Fourier Series by Juan Arias de Reyna Pdf

This book contains a detailed exposition of Carleson-Hunt theorem following the proof of Carleson: to this day this is the only one giving better bounds. It points out the motivation of every step in the proof. Thus the Carleson-Hunt theorem becomes accessible to any analyst.The book also contains the first detailed exposition of the fine results of Hunt, Sjölin, Soria, etc on the convergence of Fourier Series. Its final chapters present original material. With both Fefferman's proof and the recent one of Lacey and Thiele in print, it becomes more important than ever to understand and compare these two related proofs with that of Carleson and Hunt. These alternative proofs do not yield all the results of the Carleson-Hunt proof. The intention of this monograph is to make Carleson's proof accessible to a wider audience, and to explain its consequences for the pointwise convergence of Fourier series for functions in spaces near $äcal Lü^1$, filling a well-known gap in the literature.

Author : Valery Serov
Publisher : Springer
Page : 0 pages
File Size : 48,5 Mb
Release : 2018-08-31
Category : Mathematics
ISBN : 3319879855

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Fourier Series, Fourier Transform and Their Applications to Mathematical Physics by Valery Serov Pdf

This text serves as an introduction to the modern theory of analysis and differential equations with applications in mathematical physics and engineering sciences. Having outgrown from a series of half-semester courses given at University of Oulu, this book consists of four self-contained parts. The first part, Fourier Series and the Discrete Fourier Transform, is devoted to the classical one-dimensional trigonometric Fourier series with some applications to PDEs and signal processing. The second part, Fourier Transform and Distributions, is concerned with distribution theory of L. Schwartz and its applications to the Schrödinger and magnetic Schrödinger operations. The third part, Operator Theory and Integral Equations, is devoted mostly to the self-adjoint but unbounded operators in Hilbert spaces and their applications to integral equations in such spaces. The fourth and final part, Introduction to Partial Differential Equations, serves as an introduction to modern methods for classical theory of partial differential equations. Complete with nearly 250 exercises throughout, this text is intended for graduate level students and researchers in the mathematical sciences and engineering.

Author : Howard J. Wilcox,David L. Myers
Publisher : Courier Corporation
Page : 194 pages
File Size : 54,9 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 : Harry F. Davis
Publisher : Courier Corporation
Page : 436 pages
File Size : 55,5 Mb
Release : 2012-09-05
Category : Mathematics
ISBN : 9780486140735

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Fourier Series and Orthogonal Functions by Harry F. Davis Pdf

This incisive text deftly combines both theory and practical example to introduce and explore Fourier series and orthogonal functions and applications of the Fourier method to the solution of boundary-value problems. Directed to advanced undergraduate and graduate students in mathematics as well as in physics and engineering, the book requires no prior knowledge of partial differential equations or advanced vector analysis. Students familiar with partial derivatives, multiple integrals, vectors, and elementary differential equations will find the text both accessible and challenging. The first three chapters of the book address linear spaces, orthogonal functions, and the Fourier series. Chapter 4 introduces Legendre polynomials and Bessel functions, and Chapter 5 takes up heat and temperature. The concluding Chapter 6 explores waves and vibrations and harmonic analysis. Several topics not usually found in undergraduate texts are included, among them summability theory, generalized functions, and spherical harmonics. Throughout the text are 570 exercises devised to encourage students to review what has been read and to apply the theory to specific problems. Those preparing for further study in functional analysis, abstract harmonic analysis, and quantum mechanics will find this book especially valuable for the rigorous preparation it provides. Professional engineers, physicists, and mathematicians seeking to extend their mathematical horizons will find it an invaluable reference as well.

Author : Godfrey Harold Hardy,Werner Rogosinski
Publisher : Courier Corporation
Page : 113 pages
File Size : 48,7 Mb
Release : 1999-01-01
Category : Mathematics
ISBN : 9780486406817

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Fourier Series by Godfrey Harold Hardy,Werner Rogosinski Pdf

Geared toward mathematicians already familiar with the elements of Lebesgue's theory of integration, this classic graduate-level text begins with a brief introduction to some generalities of trigonometrical series. Discussions of the Fourier series in Hilbert space lead to an examination of further properties of trigonometrical Fourier series and related subjects. 1956 edition.

Author : William Elwood Byerly
Publisher : Unknown
Page : 312 pages
File Size : 54,7 Mb
Release : 1893
Category : Electronic
ISBN : RUTGERS:39030016181598

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An elementary treatise on Fourier's series and spherical, cylindrical... by William Elwood Byerly Pdf

Author : Ferenc Weisz
Publisher : Springer Nature
Page : 299 pages
File Size : 45,6 Mb
Release : 2021-06-12
Category : Mathematics
ISBN : 9783030746360

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Lebesgue Points and Summability of Higher Dimensional Fourier Series by Ferenc Weisz Pdf

This monograph presents the summability of higher dimensional Fourier series, and generalizes the concept of Lebesgue points. Focusing on Fejér and Cesàro summability, as well as theta-summation, readers will become more familiar with a wide variety of summability methods. Within the theory of higher dimensional summability of Fourier series, the book also provides a much-needed simple proof of Lebesgue’s theorem, filling a gap in the literature. Recent results and real-world applications are highlighted as well, making this a timely resource. The book is structured into four chapters, prioritizing clarity throughout. Chapter One covers basic results from the one-dimensional Fourier series, and offers a clear proof of the Lebesgue theorem. In Chapter Two, convergence and boundedness results for the lq-summability are presented. The restricted and unrestricted rectangular summability are provided in Chapter Three, as well as the sufficient and necessary condition for the norm convergence of the rectangular theta-means. Chapter Four then introduces six types of Lebesgue points for higher dimensional functions. Lebesgue Points and Summability of Higher Dimensional Fourier Series will appeal to researchers working in mathematical analysis, particularly those interested in Fourier and harmonic analysis. Researchers in applied fields will also find this useful.

Author : William Elwood Byerly
Publisher : Unknown
Page : 312 pages
File Size : 46,6 Mb
Release : 1893
Category : Fourier series
ISBN : HARVARD:CL1KEK

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An Elementary Treatise on Fourier's Series and Spherical, Cylindrical, and Ellipsoidal Harmonics by William Elwood Byerly Pdf

Author : Phil Dyke
Publisher : Springer Science & Business Media
Page : 325 pages
File Size : 42,9 Mb
Release : 2014-03-24
Category : Mathematics
ISBN : 9781447163954

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An Introduction to Laplace Transforms and Fourier Series by Phil Dyke Pdf

In this book, there is a strong emphasis on application with the necessary mathematical grounding. There are plenty of worked examples with all solutions provided. This enlarged new edition includes generalised Fourier series and a completely new chapter on wavelets. Only knowledge of elementary trigonometry and calculus are required as prerequisites. An Introduction to Laplace Transforms and Fourier Series will be useful for second and third year undergraduate students in engineering, physics or mathematics, as well as for graduates in any discipline such as financial mathematics, econometrics and biological modelling requiring techniques for solving initial value problems.

Author : William Elwood Byerly
Publisher : Unknown
Page : 324 pages
File Size : 50,8 Mb
Release : 1893
Category : Fourier series
ISBN : PSU:000003568750

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An Elemenatary Treatise on Fourier's Series, and Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics by William Elwood Byerly Pdf

Author : Tim Hsu
Publisher : American Mathematical Soc.
Page : 354 pages
File Size : 40,6 Mb
Release : 2020-02-10
Category : Education
ISBN : 9781470451455

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Fourier Series, Fourier Transforms, and Function Spaces: A Second Course in Analysis by Tim Hsu Pdf

Fourier Series, Fourier Transforms, and Function Spaces is designed as a textbook for a second course or capstone course in analysis for advanced undergraduate or beginning graduate students. By assuming the existence and properties of the Lebesgue integral, this book makes it possible for students who have previously taken only one course in real analysis to learn Fourier analysis in terms of Hilbert spaces, allowing for both a deeper and more elegant approach. This approach also allows junior and senior undergraduates to study topics like PDEs, quantum mechanics, and signal processing in a rigorous manner. Students interested in statistics (time series), machine learning (kernel methods), mathematical physics (quantum mechanics), or electrical engineering (signal processing) will find this book useful. With 400 problems, many of which guide readers in developing key theoretical concepts themselves, this text can also be adapted to self-study or an inquiry-based approach. Finally, of course, this text can also serve as motivation and preparation for students going on to further study in analysis.