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Sturm-Liouville Theory and its Applications (Springer Undergraduate Mathematics Series)

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en Limba Engleză Paperback – 15 Jan 2008
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–Arzelà 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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Specificații

ISBN-13: 9781846289712
ISBN-10: 1846289718
Pagini: 272
Ilustrații: X, 264 p.
Dimensiuni: 178 x 254 x 13 mm
Greutate: 0.53 kg
Ediția: 2008
Editura: SPRINGER LONDON
Colecția Springer
Seria Springer Undergraduate Mathematics Series

Locul publicării: London, United Kingdom

Public țintă

Lower undergraduate

Cuprins

Inner Product Space.- The Sturm–Liouville Theory.- Fourier Series.- Orthogonal Polynomials.- Bessel Functions.- The Fourier Transformation.- The Laplace Transformation.

Recenzii

From the reviews:
"As this book amply demonstrates, Sturm-Liouville theory, a special topic within ordinary different equations, affords the student a nearly perfect case-study-type initiation into higher mathematics. … Summing Up: Recommended. General readers, undergraduates, professionals." (D. V. Feldman, Choice, Vol. 46 (2), October, 2008)

Notă biografică

Mohammed Algwaiz is Professor of Mathematics at King Saud University, Riyadh, and an experienced author having written Theory of Distributions for Marcel Dekker (vol 159, 1992, New York) and five books in Arabic on complex, real and Fourier analysis. He is also involved in developing public school curricula and textbooks for the Ministry of Education in Saudi Arabia.

Textul de pe ultima copertă

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–Arzelà 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. 

Caracteristici

Provides a rigorous introduction to the theory at a level suitable for undergraduates
Includes plenty of clearly-worked examples and exercises with solutions thereby making the book well-suited for self-study
Designed to accompany a one-semester course, the book will prepare readers for a course on PDEs
Includes supplementary material: sn.pub/extras
Request lecturer material: sn.pub/lecturer-material