Applied Partial Differential Equations (Undergraduate Texts in Mathematics)

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 equations of mathematical physics (e.g., the heat equation, the wave equation, and Laplace's equation) and methods for solving those equations on bounded and unbounded domains (including transform methods and eigenfunction expansions). Prerequisites include multivariable calculus and post- calculus differential equations course. 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 writing has an engineering and science style to it rather than a traditional, mathematical, theorem-proof format. The exercises encourage students to think about the concepts and derivations. The student who reads this book carefully and solves most of the exercises will have a sound enough knowledge base to continue with a second-year partial differential equations course where careful proofs are constructed or upper division courses in science and in egineering where detailed applications of partial differential equations are introduced.

This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory.

This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of the exercises will have a sound knowledge base for upper division mathematics, science, and engineering courses where detailed models and applications are introduced.

J. David Logan is Professor of Mathematics at University of Nebraska, Lincoln. He is also the author of numerous books, including Transport Modeling in Hydrogeochemical Systems (Springer 2001).