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© 2004

Applied Partial Differential Equations

  • The text differs from other texts in that it is a brief treatment

  • 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

Textbook

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. J. David Logan
    Pages 96-120
  3. Back Matter
    Pages 197-212

About this book

Introduction

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).

Keywords

biology Boundary value problem differential equation mathematical physics ordinary differential equation partial differential equation solution standard model wave equation

Authors and affiliations

  1. 1.Department of MathematicsUniversity of Nebraska at LincolnLincolnUSA

Bibliographic information

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Reviews

From the reviews of the second edition:

"This second edition of the short undergraduate text provides a fist course in PDE aimed at students in mathematics, engineering and the sciences. The material is standard … . Strong emphasis is put on modeling and applications throughout; the main text is supplied with many examples and exercises." (R. Steinbauer, Monatshefte für Mathematik, Vol. 150 (4), 2007)

"This book contains an elementary introduction of partial differential equations to undergraduate students in mathematics, engineering, and physical sciences. … This is a unique book in the sense that it provides a coverage of the main topics of the subject in a concise style which is accessible to science and engineering students. … Reading this book and solving the problems, the students will have a solid base for a course in partial differential equations … ." (Tibor Krisztin, Acta Scientiarum Mathematicarum, Vol. 74, 2008)