Applied Partial Differential Equations

  • J. David Logan

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

  • J. David Logan
    • 1
  1. 1.Department of MathematicsUniversity of Nebraska-LincolnLincolnUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-12493-3
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-12492-6
  • Online ISBN 978-3-319-12493-3
  • Series Print ISSN 0172-6056
  • Series Online ISSN 2197-5604
  • About this book