Applied Partial Differential Equations: With Fourier Series and Boundary Value Problems, 4th Edition

by Richard Haberman

Emphasizing the physical interpretation of mathematical solutions, this book introduces applied mathematics while presenting partial differential equations. Topics addressed include heat equation, method of separation of variables, Fourier series, Sturm-Liouville eigenvalue problems, finite difference numerical methods for partial differential equations, nonhomogeneous problems, Green's functions for time-independent problems, infinite domain problems, Green's functions for wave and heat equations, the method of characteristics for linear and quasi-linear wave equations and a brief introduction to Laplace transform solution of partial differential equations. For scientists and engineers.

Genres: Mathematics, Science, Textbooks, Nonfiction

769 pages, Hardcover

First published April 5, 2003

Reviews

[Tomáš Ševček · Rating 5 out of 5]

I find this book to be a clearly written introductory text on PDEs for applied mathematicians. I only read certain parts of this book since I studied PDEs mostly from Evans (which is in my opinion more suitable for pure/general mathematicians). The book covers the basic techniques for studying PDEs - transform and series methods, separation of variables, characteristics, Green's functions and so on. It also contains some more advanced topics such as dispersive waves, pattern formation or perturbation methods. It even contains a chapter on numerical analysis of PDEs, namely on the finite difference method (finite elements are briefly discussed as well). The prerequisites are a good knowledge of calculus (single-variable, multi-variable as well as vector) and ODEs. The book contains chapters on Fourier series and Sturm-Liouville problems (even showing how to qualitative analyze eigenvalues), so there is no need to be familiar with those beforehand. Unlike Evans, the book focuses on problems and applications of PDEs, not on theorems and proofs and no real knowledge of functional analysis is required. On the one hand, this makes the book more accessible to a wider audience. On the other hand, some of the more advanced topics requiring functional analysis are merely glossed over or explained very superficially (such as finite elements). That being said, the book shows you how to derive PDEs of real-world phenomena (albeit in the 'classical' sense so, for instance, the heat equation is only derived making use of Fourier's/Fick's law and not of Brownian motion), which cannot be found in Evans. I definitely recommend the book to anyone interested in studying real-world problems with PDEs but also as a complement for people reading Evans to see the applied side of PDEs.

[John Ledesma]

This subject really excites me.