Al-Gwaiz Sturm-Liouville Theory and its Applications

2008
ISBN: 978-1-84628-972-9
Verlag: Springer
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 266 Seiten, eBook

Reihe: Springer Undergraduate Mathematics Series

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 L
2
. 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.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Al-Gwaiz, Mohammed

Inhaltsverzeichnis

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

Über Autor(innen)

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.