Undergraduate textbooks on Fourier series which follow a pointwise approach to convergence miss the rich geometric content which comes with treating the subject within the inner product space L2. This book, developed from a course taught to senior undergraduates, provides a unified introduction to Fourier analysis and special functions based on the Sturm-Liouville theory in L2. The basic results of this theory, namely the orthogonality and completeness of its eigenfunctions, are established in Chapter 2; the remaining ...
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Undergraduate textbooks on Fourier series which follow a pointwise approach to convergence miss the rich geometric content which comes with treating the subject within the inner product space L2. This book, developed from a course taught to senior undergraduates, provides a unified introduction to Fourier analysis and special functions based on the Sturm-Liouville theory in L2. The basic results of this theory, namely the orthogonality and completeness of its eigenfunctions, are established in Chapter 2; the remaining chapters present examples and applications. The last two chapters, on Fourier and Laplace transformations, while not part of the Sturm-Liouville theory, extend the Fourier series method for representing functions to integral representations. The treatment relies heavily on the convergence properties of sequences and series of numbers as well as functions, and assumes a solid background in advanced calculus and an acquaintance with ordinary differential equations and linear algebra. Familiarity with the relevant theorems of real analysis, such as the Ascoli-Arzela theorem, is also useful for following the proofs. The presentation follows a clear and rigorous mathematical style that is both readable and well motivated, with many examples and applications used to illustrate the theory. Although addressed primarily to undergraduate students of mathematics, the book will also be of interest to students in related disciplines, such as physics and engineering, where Fourier analysis and special functions are used extensively for solving linear differential equations.
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Add this copy of Sturm-Liouville Theory and Its Applications to cart. $53.47, fair condition, Sold by Anybook rated 5.0 out of 5 stars, ships from Lincoln, UNITED KINGDOM, published 2008 by Springer.
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This is an ex-library book and may have the usual library/used-book markings inside. This book has soft covers. Clean from markings. In fair condition, suitable as a study copy. Please note the Image in this listing is a stock photo and may not match the covers of the actual item, 550grams, ISBN: 9781846289712.
Add this copy of Sturm-Liouville Theory and Its Applications (Springer to cart. $64.32, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2007 by Springer.
Add this copy of Sturm-Liouville Theory and Its Applications (Springer to cart. $99.20, new condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2007 by Springer.
