Fourier Analysis With Applications
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Fourier Analysis with Applications
Author | : Adrian Constantin |
Publsiher | : Cambridge University Press |
Total Pages | : 368 |
Release | : 2016-06-02 |
Genre | : Mathematics |
ISBN | : 9781107044104 |
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A two-volume advanced text for graduate students. This first volume covers the theory of Fourier analysis.
Fourier Analysis and Its Applications
Author | : G. B. Folland |
Publsiher | : American Mathematical Soc. |
Total Pages | : 447 |
Release | : 2009 |
Genre | : Fourier analysis |
ISBN | : 9780821847909 |
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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.
Fourier Analysis and Its Applications
Author | : Anders Vretblad |
Publsiher | : Springer Science & Business Media |
Total Pages | : 270 |
Release | : 2003-07-17 |
Genre | : Mathematics |
ISBN | : 9780387008363 |
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This book presents the basic ideas in Fourier analysis and its applications to the study of partial differential equations. It also covers the Laplace and Zeta transformations and the fundaments of their applications. The author has intended to make his exposition accessible to readers with a limited background, for example, those not acquainted with the Lebesgue integral or with analytic functions of a complex variable. At the same time, he has included discussions of more advanced topics such as the Gibbs phenomenon, distributions, Sturm-Liouville theory, Cesaro summability and multi-dimensional Fourier analysis, topics which one usually will not find in books at this level. Many of the chapters end with a summary of their contents, as well as a short historical note. The text contains a great number of examples, as well as more than 350 exercises. In addition, one of the appendices is a collection of the formulas needed to solve problems in the field. Anders Vretblad is Senior Lecturer of Mathematics at Uppsala University, Sweden.
Fourier Analysis and Its Applications
Author | : Anders Vretblad |
Publsiher | : Springer Science & Business Media |
Total Pages | : 275 |
Release | : 2006-04-18 |
Genre | : Mathematics |
ISBN | : 9780387217239 |
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A carefully prepared account of the basic ideas in Fourier analysis and its applications to the study of partial differential equations. The author succeeds to make his exposition accessible to readers with a limited background, for example, those not acquainted with the Lebesgue integral. Readers should be familiar with calculus, linear algebra, and complex numbers. At the same time, the author has managed to include discussions of more advanced topics such as the Gibbs phenomenon, distributions, Sturm-Liouville theory, Cesaro summability and multi-dimensional Fourier analysis, topics which one usually does not find in books at this level. A variety of worked examples and exercises will help the readers to apply their newly acquired knowledge.
The Fourier Transform and Its Applications
Author | : Ronald Newbold Bracewell |
Publsiher | : Unknown |
Total Pages | : 135 |
Release | : 1978 |
Genre | : Fourier transformations |
ISBN | : OCLC:220097501 |
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Theory and Applications of Fourier Analysis
Author | : Charles Sparks Rees,S. M. Shah,Caslav V. Stanojevic |
Publsiher | : CRC Press |
Total Pages | : 432 |
Release | : 1981-01-01 |
Genre | : Mathematics |
ISBN | : 0824769031 |
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Trignometric sums; Integrability of trigonometric sums; Convergence and cesaro summability of fourier series; Convergence and summability of trigonetric series; Multiple fourier series; Fourier transform and applications; Orthogonal systems; Bessel functions.
Real Analysis and Applications
Author | : Frank Morgan |
Publsiher | : American Mathematical Society |
Total Pages | : 209 |
Release | : 2021-10-25 |
Genre | : Mathematics |
ISBN | : 9781470465018 |
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Real Analysis and Applications starts with a streamlined, but complete approach to real analysis. It finishes with a wide variety of applications in Fourier series and the calculus of variations, including minimal surfaces, physics, economics, Riemannian geometry, and general relativity. The basic theory includes all the standard topics: limits of sequences, topology, compactness, the Cantor set and fractals, calculus with the Riemann integral, a chapter on the Lebesgue theory, sequences of functions, infinite series, and the exponential and Gamma functions. The applications conclude with a computation of the relativistic precession of Mercury's orbit, which Einstein called "convincing proof of the correctness of the theory [of General Relativity]." The text not only provides clear, logical proofs, but also shows the student how to come up with them. The excellent exercises come with select solutions in the back. Here is a text which makes it possible to do the full theory and significant applications in one semester. Frank Morgan is the author of six books and over one hundred articles on mathematics. He is an inaugural recipient of the Mathematical Association of America's national Haimo award for excellence in teaching. With this applied version of his Real Analysis text, Morgan brings his famous direct style to the growing numbers of potential mathematics majors who want to see applications right along with the theory.
Fourier Analysis and Applications
Author | : Claude Gasquet,Patrick Witomski |
Publsiher | : Springer Science & Business Media |
Total Pages | : 434 |
Release | : 2013-12-01 |
Genre | : Mathematics |
ISBN | : 9781461215981 |
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The object of this book is two-fold -- on the one hand it conveys to mathematical readers a rigorous presentation and exploration of the important applications of analysis leading to numerical calculations. On the other hand, it presents physics readers with a body of theory in which the well-known formulae find their justification. The basic study of fundamental notions, such as Lebesgue integration and theory of distribution, allow the establishment of the following areas: Fourier analysis and convolution Filters and signal analysis time-frequency analysis (gabor transforms and wavelets). The whole is rounded off with a large number of exercises as well as selected worked-out solutions.