Developed from a course taught to senior undergraduates, this book provides aunified 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 assumesa solid background in advanced calculus and an acquaintance with ordinary differential equations and linear algebra. Familiarity with the relevant theoremsof 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. Provides a rigorous introduction to the theory at a level suitable for undergraduates INDICE: Inner product space.- The Sturm-Liouville theory.- Fourier series.- Orthogonal polynomials.- Bessel functions.- The Fourier transformation.- TheLaplace transformation.- Solutions to selected exercises.- References.- Notation.- Index.
- ISBN: 978-1-84628-971-2
- Editorial: Springer
- Encuadernacion: Rústica
- Páginas: 264
- Fecha Publicación: 01/01/2008
- Nº Volúmenes: 1
- Idioma: Inglés