Analytic Methods for Partial Differential Equations
By: by Gwynne A. Evans, Jonathan M. Blackledge, Peter D. Yardley
Contributors: Blackledge, J. M. (Jonathan M.); Yardley, Peter D.
Series: Springer Undergraduate Mathematics Series, 1615-2085; Springer undergraduate mathematics series
Publisher: Springer London; Imprint; Springer
Published: 1999
Place of publication: London
Language: eng
Format: [electronic resource] /
Number of pages: 316
ISBN-13: 9781447103790
Subjects: Mathematics; Numerical analysis; Global analysis (Mathematics)
Description: The subject of partial differential equations holds an exciting place in mathematics. At one extreme the interest lies in the existence and uniqueness of solutions, and the functional analysis of the proofs of these properties. At the other extreme lies the applied mathematical and engineering quest to find useful solutions, either analytically or numerically, to these important equations which can be used in design and construction. The objective of this book is to actually solve equations rather than discuss the theoretical properties of their solutions. The topics are approached practically, without losing track of the underlying mathematical foundations of the subject. The topics covered include the separation of variables, the characteristic method, D'Alembert's method, integral transforms and Green's functions. Numerous exercises are provided as an integral part of the learning process, with solutions provided in a substantial appendix.
Table of contents: title: Mathematical Preliminaries; title: Separation of the Variables; title: First Order Equations and Hyperbolic Second Order Equations; title: Integral Transform Methods; title: Green's Functions; title: Appendix; title: References; title: Index.