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. 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.
Intended for a one-semester undergraduate course, the book includes numerous exercises, with solutions to selected exercises provided and a full solutions manual available for course instructors. 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. Familiarity with the relevant theorems of real analysis, such as the Ascoli-Arzela theorem and the dominated convergence theorem, are also useful for following the proofs.
1 Inner Product Space.- 2 The SturmLiouville Theory.- 3 Fourier
Series.- 4 Orthogonal Polynomials.- 5 Bessel Functions.- 6 The Fourier
Transformation.- 7 The Laplace Transformation.
M.A. Al-Gwaiz is a professor of Mathematics at King Saud University, Riyadh, and an accomplished author having written Theory of Distributions for Marcel Dekker (vol 159, 1992, New York) and six books in Arabic on complex, real and Fourier analysis as well as partial differential equations. He was also involved in developing public school curricula and textbooks for the Ministry of Education in Saudi Arabia.
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