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

Al-Gwaiz, M. A.

Springer（2007/12発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 265 p.／サイズ 25 illus.
• 言語 ENG
• 商品コード 9781846289712
• DDC分類 515.35

基本説明

Provides a rigorous introduction to the theory at a level suitable for undergraduates; Includes plenty of clearly-worked examples and exercises with solutions.

Full Description

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.

Contents

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