Overview
- 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
Part of the book series: Springer Undergraduate Mathematics Series (SUMS)
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Table of contents (7 chapters)
Keywords
About this book
Developed from a course taught to senior undergraduates, this book provides a unified introduction to Fourier analysis and special functions based on the Sturm-Liouville theory in L2. 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.
Reviews
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)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Sturm-Liouville Theory and its Applications
Authors: M. A. Al-Gwaiz
Series Title: Springer Undergraduate Mathematics Series
DOI: https://doi.org/10.1007/978-1-84628-972-9
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London 2008
Softcover ISBN: 978-1-84628-971-2Published: 15 January 2008
eBook ISBN: 978-1-84628-972-9Published: 21 November 2007
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
Edition Number: 1
Number of Pages: X, 264
Topics: Analysis, Functional Analysis, Special Functions, Ordinary Differential Equations, Mathematical and Computational Engineering, Mathematical Methods in Physics