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© 2015

Applied Partial Differential Equations

Textbook

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

Table of contents

  1. Front Matter
    Pages i-xi
  2. J. David Logan
    Pages 127-154
  3. J. David Logan
    Pages 229-255
  4. J. David Logan
    Pages 257-277
  5. Back Matter
    Pages 279-289

About this book

Introduction

This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs.  Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this third edition covering 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. In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science. The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course.

The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems. Many exercises and worked examples have been added to this edition. Prerequisites include calculus and ordinary differential equations. A student who reads this book and works many of the exercises will have a sound knowledge for a second course in partial differential equations or for courses in advanced engineering and science. Two additional chapters include short introductions to applications of PDEs in biology and a new chapter to the computation of solutions. A brief appendix reviews techniques from ordinary differential equations.

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 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

Keywords

Crank-Nicolson scheme Fick's law Fourier method Fourier series Gauss-Seidel method Green's identity Lagrange identity Laplace transform Leibniz rule McKendrick-von Forester equation PDE textbook adoption Sturm-Liouville problem applied PDE text d'Alembert's formula orthogonal expansion von Neumann stability analysis

Authors and affiliations

  1. 1.Department of MathematicsUniversity of Nebraska-LincolnLincolnUSA

About the authors

J. David Logan is Willa Cather Professor of Mathematics at the University of Nebraska Lincoln. He received his PhD from The Ohio State University and has served on the faculties at the University of Arizona, Kansas State University, and Rensselaer Polytechnic Institute. For many years he served as a visiting scientist at Los Alamos and Lawrence Livermore National Laboratories. He has published widely in differential equations, mathematical physics, fluid and gas dynamics, hydrogeology, and mathematical biology. Dr. Logan has authored 7 books, among them A First Course in Differential Equations, 2nd ed., published by Springer.

Bibliographic information

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Reviews

“The aim of this book is to provide the reader with basic ideas encountered in partial differential equations. … The mathematical content is highly motivated by physical problems and the emphasis is on motivation, methods, concepts and interpretation rather than formal theory. The textbook is a valuable material for undergraduate science and engineering students.” (Marius Ghergu, zbMATH 1310.35001, 2015)