Fourier Analysis and Boundary Value Problems
- Enrique Gonzalez-Velasco, University of Massachusetts
Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics.A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field.View full description
Students in courses on Fourier analysis, Fourier series, partial differential equations, and/or boundary value problems. These courses are taken by students majoring in engineering, physics, and mathematics. The audience also includes practicing engineers and mathematicians who will use the book as a reference. Prerequisites are calculus and a course in ordinary differential equations.
- Published: November 1996
- Imprint: ACADEMIC PRESS
- ISBN: 978-0-12-289640-8
"This is a lovely book. I would want to have it on my shelf as a serious Fourier Analyst...For history and mathematics this book rates very high both in scholarship and exposition...I would insist on my library getting it. It starts carefully and moves ahead to advanced material including Lebesgue integration."
--John Gilbert, University of Texas
"Gonzalez-Velasco makes historical development of the subject a major theme. For me this makes the book very interesting...this interweaving of history, integration, and PDE/BVP reads very nicely...Plenty of good exercises...very well written."--Keith Phillips, University of Colorado, Colorado Springs
Table of ContentsA Heated Discussion. Fourier Series. Return to the Heated Bar. Generalized Fourier Series. The Wave Equation. Orthogonal Systems. Fourier Transforms. Laplace Transforms. Boundary Value Problems in Higher Dimensions. Boundary Value Problems with Circular Symmetry. Boundary Value Problems with Spherical Symmetry. Uniform Convergence. Improper Integrals. Tables of Fourier and Laplace Transforms. Historical Bibliography. Index.