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 physical sciences. The topics include derivations of some of the standard models of mathematical physics (e. g. , the heat equation, the wave equation, and Laplace's equation) and methods for solving those equations on unbounded and bounded domains (transform methods and eigenfunction expansions). Prerequisites include multivariable calculus and elementary differential equations. The text differs from other texts in that it is a brief treatment (about 200 pages); 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. The many exercises help students sharpen their computational skills by encouraging them to think about concepts and derivations. The student who reads this book carefully and solves most of the problems will have a sound knowledge base for a second-year partial differential equations course where careful proofs are constructed or upper division courses in science and in engineering where detailed applications of partial differential equations are introduced.

Genres: Mathematics

181 pages, Hardcover

First published June 19, 1998

Reviews

[Tomáš Ševček]

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.