المصدر: Books in Fourier Analysis في منتدى : قسم الرياضيات by James W Brown, R V.Churchill Publisher: Mcgraw-Hill College Number Of Pages: 320 Publication Date: 1993-01-01 ISBN-10 / ASIN: 0070082022 ISBN-13 / EAN: 9780070082021 Binding: Hardcover Book Description: This is an introductory treatment of Fourier series and their applications to boundary value problems in partial differential equations of engineering and physics It is designed for students who have completed a first course in ordinary differential equations and the equivalent of a term of advanced calculus. In order that the book be accessible to as many students as possible, there are footnotes referring to texts which give proofs of the more delicate results in advanced calculus that are occasionally needed. The physical applications, explained in some detail, are kept on a fairly elementary level. The first objective of the book is to introduce the concept of orthogonal sets of functions and representations of arbitrary functions in series of functions from such sets. Representations of functions by Fourier series involving sine and cosine functions are given special attention. Fourier integral representations and expansions in series of Bessel functions and Legendre polynomials are also treated. The second objective is a clear presentation of the classical method of separations of variables used in solving boundary value problems with the aid of those representations. Some attention is given to the verification of solutions and to uniqueness of solutions, for the method cannot be presented properly without such considerations. Other methods are treated in the authors' book Complex Variables and Applications, and in Professor Churchill's book, Operational Mathematics or The Fourier Transform & Its Applications By Ronald N. Bracewell Publisher: McGraw-Hill Science Number Of Pages: 640 Publication Date: 1999-06-08 ISBN-10 / ASIN: 0073039381 ISBN-13 / EAN: 9780073039381 Binding: Hardcover Product Description: This text is designed for use in a senior undergraduate or graduate level course in Fourier Transforms. This text differs from many other fourier transform books in its emphasis on applications. Bracewell applies mathematical concepts to the physical world throughout this text, equipping students to think about the world and physics in terms of transforms. The pedagogy in this classic text is excellent. The author has included such tools as the pictorial dictionary of transforms and bibliographic references. In addition, there are many excellent problems throughout this book, which are more than mathematical exercises, often requiring students to think in terms of specific situations or asking for educated opinions. To aid students further, discussions of many of the problems can be found at the end of the book. or Fourier Analysis: An Introduction (Princeton Lectures in Analysis, Volume 1) By Elias M. Stein, Rami Shakarchi Publisher: Princeton University Press Number Of Pages: 320 Publication Date: 2003-03-17 ISBN-10 / ASIN: 069111384X ISBN-13 / EAN: 9780691113845 Binding: Hardcover Product Description: 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. or
(Studies in Advanced Mathematics) by Kenneth B. Howell Publisher: CRC Number Of Pages: 792 Publication Date: 2001-05-18 Sales Rank: 877037 ISBN / ASIN: 0849382750 EAN: 9780849382758 Binding: Hardcover Manufacturer: CRC Studio: CRC Average Rating: 5 Total Reviews: 2 Book Description: 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. or
Fourier Analysis and Boundary Value Problems By Enrique A. Gonzalez-Velasco Publisher: Academic Press Number Of Pages: 551 Publication Date: 1995-01-15 ISBN-10 / ASIN: 0122896408 ISBN-13 / EAN: 9780122896408 Binding: Hardcover Book Description: Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics. A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field. or
Exercises in Fourier Analysis By T. W. Körner Publisher: Cambridge University Press Number Of Pages: 395 Publication Date: 1993-09-24 ISBN-10 / ASIN: 0521438497 ISBN-13 / EAN: 9780521438490 Binding: Paperback Book Description: Fourier analysis is an indispensable tool for physicists, engineers and mathematicians. A wide variety of the techniques and applications of fourier analysis are discussed in Dr. Körner's highly popular book, An Introduction to Fourier Analysis (1988). In this book, Dr. Körner has compiled a collection of exercises on Fourier analysis that will thoroughly test the reader's understanding of the subject. They are arranged chapter by chapter to correspond with An Introduction to Fourier Analysis, and for all who enjoyed that book, this companion volume will be an essential purchase. or
Fourier Series (Classroom Resource Materials) By Rajendra Bhatia Publisher: The Mathematical Association of America Number Of Pages: 120 Publication Date: 2004-12-15 ISBN-10 / ASIN: 0883857405 ISBN-13 / EAN: 9780883857403 Binding: Hardcover Book Description: 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.
Discrete and Continuous Fourier Transforms: Analysis, Applications and Fast Algorithms By Eleanor Chu Publisher: Chapman & Hall/CRC Number Of Pages: 424 Publication Date: 2008-03-19 ISBN-10 / ASIN: 1420063634 ISBN-13 / EAN: 9781420063639 Binding: Hardcover Product Description: Long employed in electrical engineering the discrete Fourier transform (DFT) is now applied in a range of fields through the use of digital computers and fast Fourier transform (FFT) algorithms. But to correctly interpret DFT results, it is essential to understand the core and tools of Fourier analysis. Discrete and Continuous Fourier Transforms: Analysis, Applications and Fast Algorithms presents the fundamentals of Fourier analysis and their deployment in signal processing using DFT and FFT algorithms. This accessible, self-contained book provides meaningful interpretations of essential formulas in the context of applications, building a solid foundation for the application of Fourier analysis in the many diverging and continuously evolving areas in digital signal processing enterprises. It comprehensively covers the DFT of windowed sequences, various discrete convolution algorithms and their applications in digital filtering and filters, and many FFT algorithms unified under the frameworks of mixed-radix FFTs and prime factor FFTs. A large number of graphical illustrations and worked examples help explain the concepts and relationships from the very beginning of the text. Requiring no prior knowledge of Fourier analysis or signal processing, this book supplies the basis for using FFT algorithms to compute the DFT in a variety of application areas.
Part I Distributions and Fourier Transforms (Introduction to the theory of Distributions) Part II (Introduction to Fourier Transforms). [Lecture Notes] by Olga Goncharova Author: Olga Goncharova Lecture notes title: Distributions and Fourier transforms Winter term 2001-2002 Part I, Introduction to the Theory of Distributions Contents 1- The concepts of Distributions 2- Test functions 3- Distributions Part II, Introduction to Fourier Transforms Contents 1- Fourier Series and Fourier Transforms 2- Fourier - Transforms 3- Distribution Solutions to Differential Equations 4- Partial Differential Equations 5- Fourier Analysis Password: gigapedia.org
