Applied Partial Differential Equations

by J. David Logan

This textbook is for the standard, one-semester, junior-senior course that often goes by the title "Elementary Partial Differential Equations" or "Boundary Value Problems". The audience consists of students in mathematics, engineering, and the sciences. The topics include derivations of some of the standard models of mathematical physics and methods for solving those equations on unbounded and bounded domains, and applications of PDE's to biology. The text differs from other texts in its brevity; yet it provides coverage of the main topics usually studied in the standard course, as well as an introduction to using computer algebra packages to solve and understand partial differential equations. For the 3rd edition the section on numerical methods has been considerably expanded to reflect their central role in PDE's. A treatment of the finite element method has been included and the code for numerical calculations is now written for MATLAB. Nonetheless the brevity of the text has been maintained. To further aid the reader in mastering the material and using the book, the clarity of the exercises has been improved, more routine exercises have been included, and the entire text has been visually reformatted to improve readability.

Genres: Mathematics

300 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.