This book provides a unified introduction to Fourier analysis and special functions based on the Sturm-Liouville theory in L 2 . The author establishes the basic results of Sturm-Liouville theory and then provides plenty of examples and applications.

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 AscoliArzelà 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.

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

Autorentext
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.

Klappentext

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 L 2 . 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 L 2 . 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 AscoliArzelà 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.

Inhalt
Inner Product Space.- The SturmLiouville Theory.- Fourier Series.- Orthogonal Polynomials.- Bessel Functions.- The Fourier Transformation.- The Laplace Transformation.