Download or read book Fourier Series Fourier Transform and Their Applications to Mathematical Physics written by Valery Serov and published by Springer. This book was released on 2018-08-31 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Fourier Series Fourier Transform and Their Applications to Mathematical Physics written by Valery Serov and published by . This book was released on 2020-12-17 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier Series, Fourier Transform and Their Applications to Mathematical Physics : Applied Mathematical Sciences by Valery SerovThe modern theory of analysis and differential equations in general certainly in-cludes the Fourier transform, Fourier series, integral operators, spectral theory ofdifferential operators, harmonic analysis and much more. This book combines allthese subjects based on a unified approach that uses modern view on all thesethemes. The book consists of four parts: Fourier series and the discrete Fouriertransform, Fourier transform and distributions, Operator theory and integral equa-tions and Introduction to partial differential equations and it outgrew from the half-semester courses of the same name given by the author at University of Oulu, Fin-land during 2005-2015.Each part forms a self-contained text (although they are linked by a commonapproach) and can be read independently. The book is designed to be a modernintroduction to qualitative methods used in harmonic analysis and partial differentialequations (PDEs). It can be noted that a survey of the state of the art for all parts ofthis book can be found in a very recent and fundamental work of B. Simon [35].This book contains about 250 exercises that are an integral part of the text. Eachpart contains its own collection of exercises with own numeration. They are not onlyan integral part of the book, but also indispensable for the understanding of all partswhose collection is the content of this book. It can be expected that a careful readerwill complete all these exercises.This book is intended for graduate level students majoring in pure and appliedmathematics but even an advanced researcher can find here very useful informationwhich previously could only be detected in scientific articles or monographs.Each part of the book begins with its own introduction which contains the facts(mostly) from functional analysis used thereinafter. Some of them are proved whilethe others are not.The first part, Fourier series and the discrete Fourier transform, is devoted tothe classical one-dimensional trigonometric Fourier series with some applicationsto PDEs and signal processing. This part provides a self-contained treatment of allwell known results (but not only) at the beginning graduate level. Compared withsome known texts (see [12, 18, 29, 35, 38, 44, 45]) this part uses many functionspaces such as Sobolev, Besov, Nikol'skii and Holder spaces. All these spaces are introduced by special manner via the Fourier coefficients and they are used in theproofs of main results. Same definition of Sobolev spaces can be found in [35]. Theadvantage of such approach is that we are able to prove quite easily the precise em-beddings for these spaces that are the same as in classical function theory (see [1, 3,26, 42]). In the frame of this part some very delicate properties of the trigonometricFourier series (Chapter 10) are considered using quite elementary proofs (see also[46]). The unified approach allows us also to consider naturally the discrete Fouriertransform and establish its deep connections with the continuous Fourier transform.As a consequence we prove the famous Whittaker-Shannon-Boas theorem about thereconstruction of band-limited signal via the trigonometric Fourier series (see Chap-ter 13). Many applications of the trigonometric Fourier series to the one-dimensionalheat, wave and Laplace equation are presented in Chapter 14. It is accompanied by alarge number of very useful exercises and examples with applications in PDEs (seealso [10, 17]).The second part, Fourier transform and distributions, probably takes a central rolein this book and it is concerned with distribution theory of L. Schwartz and its ap-plications to the Schrodinger and magnetic Schr ̈ odinger operators (see Chapter ̈ 32).

Download or read book Fourier Series Fourier Transform and Their Applications to Mathematical Physics written by Valery Serov and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Schrdinger and magnetic Schrdinger 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.

Download or read book Distributions Fourier Transforms And Some Of Their Applications To Physics written by Schucker Thomas and published by World Scientific Publishing Company. This book was released on 1991-04-22 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, distributions are introduced via sequences of functions. This approach due to Temple has two virtues:The Fourier transform is defined for functions and generalized to distributions, while the Green function is defined as the outstanding application of distributions. Using Fourier transforms, the Green functions of the important linear differential equations in physics are computed. Linear algebra is reviewed with emphasis on Hilbert spaces. The author explains how linear differential operators and Fourier transforms naturally fit into this frame, a point of view that leads straight to generalized fourier transforms and systems of special functions like spherical harmonics, Hermite, Laguerre, and Bessel functions.

Download or read book Fourier Transforms and Their Physical Applications written by D. C. Champeney and published by . This book was released on 1973 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Introduction to Fourier Analysis written by Russell L. Herman and published by CRC Press. This book was released on 2016-09-19 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book helps students explore Fourier analysis and its related topics, helping them appreciate why it pervades many fields of mathematics, science, and engineering. This introductory textbook was written with mathematics, science, and engineering students with a background in calculus and basic linear algebra in mind. It can be used as a textbook for undergraduate courses in Fourier analysis or applied mathematics, which cover Fourier series, orthogonal functions, Fourier and Laplace transforms, and an introduction to complex variables. These topics are tied together by the application of the spectral analysis of analog and discrete signals, and provide an introduction to the discrete Fourier transform. A number of examples and exercises are provided including implementations of Maple, MATLAB, and Python for computing series expansions and transforms. After reading this book, students will be familiar with: • Convergence and summation of infinite series • Representation of functions by infinite series • Trigonometric and Generalized Fourier series • Legendre, Bessel, gamma, and delta functions • Complex numbers and functions • Analytic functions and integration in the complex plane • Fourier and Laplace transforms. • The relationship between analog and digital signals Dr. Russell L. Herman is a professor of Mathematics and Professor of Physics at the University of North Carolina Wilmington. A recipient of several teaching awards, he has taught introductory through graduate courses in several areas including applied mathematics, partial differential equations, mathematical physics, quantum theory, optics, cosmology, and general relativity. His research interests include topics in nonlinear wave equations, soliton perturbation theory, fluid dynamics, relativity, chaos and dynamical systems.

Download or read book The Fourier Transform and Its Applications written by Ronald Newbold Bracewell and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Student s Guide to Fourier Transforms written by John Francis James and published by Cambridge University Press. This book was released on 2002-09-19 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier transform theory is of central importance in a vast range of applications in physical science, engineering, and applied mathematics. This new edition of a successful student text provides a concise introduction to the theory and practice of Fourier transforms, using qualitative arguments wherever possible and avoiding unnecessary mathematics. After a brief description of the basic ideas and theorems, the power of the technique is then illustrated by referring to particular applications in optics, spectroscopy, electronics and telecommunications. The rarely discussed but important field of multi-dimensional Fourier theory is covered, including a description of computer-aided tomography (CAT-scanning). The final chapter discusses digital methods, with particular attention to the fast Fourier transform. Throughout, discussion of these applications is reinforced by the inclusion of worked examples. The book assumes no previous knowledge of the subject, and will be invaluable to students of physics, electrical and electronic engineering, and computer science.

Download or read book Fourier Transforms written by Ian Naismith Sneddon and published by . This book was released on 2013-04 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Lectures on the Fourier Transform and Its Applications written by Brad G. Osgood and published by American Mathematical Soc.. This book was released on 2019-01-18 with total page 689 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is derived from lecture notes for a course on Fourier analysis for engineering and science students at the advanced undergraduate or beginning graduate level. Beyond teaching specific topics and techniques—all of which are important in many areas of engineering and science—the author's goal is to help engineering and science students cultivate more advanced mathematical know-how and increase confidence in learning and using mathematics, as well as appreciate the coherence of the subject. He promises the readers a little magic on every page. The section headings are all recognizable to mathematicians, but the arrangement and emphasis are directed toward students from other disciplines. The material also serves as a foundation for advanced courses in signal processing and imaging. There are over 200 problems, many of which are oriented to applications, and a number use standard software. An unusual feature for courses meant for engineers is a more detailed and accessible treatment of distributions and the generalized Fourier transform. There is also more coverage of higher-dimensional phenomena than is found in most books at this level.

Download or read book Fourier Series Fourier Transforms and Function Spaces A Second Course in Analysis written by Tim Hsu and published by American Mathematical Soc.. This book was released on 2020-02-10 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Integral Transforms and Their Applications Third Edition written by Lokenath Debnath and published by CRC Press. This book was released on 2014-11-07 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral Transforms and Their Applications, Third Edition covers advanced mathematical methods for many applications in science and engineering. The book is suitable as a textbook for senior undergraduate and first-year graduate students and as a reference for professionals in mathematics, engineering, and applied sciences. It presents a systematic development of the underlying theory as well as a modern approach to Fourier, Laplace, Hankel, Mellin, Radon, Gabor, wavelet, and Z transforms and their applications. New to the Third Edition New material on the historical development of classical and modern integral transforms New sections on Fourier transforms of generalized functions, the Poisson summation formula, the Gibbs phenomenon, and the Heisenberg uncertainty principle Revised material on Laplace transforms and double Laplace transforms and their applications New examples of applications in mechanical vibrations, electrical networks, quantum mechanics, integral and functional equations, fluid mechanics, mathematical statistics, special functions, and more New figures that facilitate a clear understanding of physical explanations Updated exercises with solutions, tables of integral transforms, and bibliography Through numerous examples and end-of-chapter exercises, this book develops readers’ analytical and computational skills in the theory and applications of transform methods. It provides accessible working knowledge of the analytical methods and proofs required in pure and applied mathematics, physics, and engineering, preparing readers for subsequent advanced courses and research in these areas.

Download or read book Applications of Discrete and Continuous Fourier Analysis written by H. Joseph Weaver and published by . This book was released on 1992 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Guide to Distribution Theory and Fourier Transforms written by Robert S. Strichartz and published by World Scientific. This book was released on 2003 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important book provides a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations. The author clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many problems are included. The book also introduces several significant recent topics, including pseudodifferential operators, wave front sets, wavelets, and quasicrystals. Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the concepts in the book.A Guide to Distribution Theory and Fourier Transforms can serve as a textbook for parts of a course on Applied Analysis or Methods of Mathematical Physics, and in fact it is used that way at Cornell.

Download or read book Fourier and Laplace Transforms written by and published by Cambridge University Press. This book was released on 2003-08-07 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Tables of Fourier Transforms and Fourier Transforms of Distributions written by Fritz Oberhettinger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of integrals of the sine-, cosine- and exponential Fourier transforms of functions f(x). It is the second, considerably enlarged version of the author's previous publication "Tabellen zur Fourier Transformation" (Springer-Verlag 1957). In addition to numerous new results in Parts I-III, a new Part IV has been introduced dealing with problems in mathematical statistics. The aim of the book is to serve as a reference work for all those whose main interest is in the application of Fourier transform methods. These methods have found a wide variety of applications in the natural and technical sciences.

Download or read book Fourier Analysis and Its Applications written by G. B. Folland and published by American Mathematical Soc.. This book was released on 2009 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.