Applied Partial Differential Equations

by J. David Logan

This text is written for the standard, one-semester, undergraduate course in elementary partial differential equations. The topics include derivations of some of the standard equations of mathematical physics (including the heat equation, the wave equation, and Laplace's equation) and methods for solving those equations on bounded and unbounded domains. Methods include eigenfunction expansions, or separation of variables, and methods based on Fourier and Laplace transforms.

Genres: Mathematics

212 pages, Hardcover

First published June 19, 1998

Reviews

[Tomáš Ševček · Rating 5 out of 5]

A great introduction to PDEs for applied mathematicians, which should be accessible to advanced undergraduate students as well. The book covers the basic techniques for studying PDEs (separation of variables, Duhamel's principle, transform methods). It even contains a brief overview of the finite difference method and inverse problems. The last chapter then shows the reader applications via age-structured models, traveling waves and stability of equilibria. While this book does not contain nearly as much as those by Evans, Haberman or even other books by Logan, I find the first chapter to be a real gem as it shows you how to derive PDEs in various real-world context (not only in physics, but in biology as well). The exercises (not only in that chapter) are interesting as well. Since this is an introductory text, only a good knowledge of calculus (mostly single-variable though some problems are multidimensional where multi-variable and vector calculus are needed) and ODEs is required, which makes the book potentially accessible to non-mathematicians with solid mathematical foundations. Therefore, if you are interested in PDEs and applications thereof with solid mathematical foundations, but find some of the other texts too advanced/detailed, this book might be the right option for you.