Overview
- Concise treatment of the main topics studied in a standard introductory course on partial differential equations
- Includes an expanded treatment of numerical computation with MATLAB replacement for all numerical calculations
- Increased number of worked out examples give student more concrete techniques to attack exercises
- Includes supplementary material: sn.pub/extras
Part of the book series: Undergraduate Texts in Mathematics (UTM)
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Table of contents (6 chapters)
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
- partial differential equations
About this book
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 sciences. The topics include derivations of some of the standard models of mathematical physics and methods for solving those equations on unbounded and bounded domains, and applications of PDE's to biology. The text differs from other texts in its brevity; 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.
For the 3rd edition the section on numerical methods has been considerably expanded to reflect their central role in PDE's. A treatment of the finite element method has been included and the code for numerical calculations is now written for MATLAB. Nonetheless the brevity of the text has been maintained. To further aid the reader in mastering the material and using the book, the clarity of the exercises has been improved, more routine exercises have been included, and the entire text has been visually reformatted to improve readability.
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)
Authors and Affiliations
About the author
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
Book Title: Applied Partial Differential Equations
Authors: J. David Logan
Series Title: Undergraduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-3-319-12493-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2015
Hardcover ISBN: 978-3-319-12492-6Published: 17 December 2014
Softcover ISBN: 978-3-319-30769-5Published: 17 December 2014
eBook ISBN: 978-3-319-12493-3Published: 05 December 2014
Series ISSN: 0172-6056
Series E-ISSN: 2197-5604
Edition Number: 3
Number of Pages: XI, 289
Number of Illustrations: 45 b/w illustrations, 6 illustrations in colour
Topics: Partial Differential Equations, Mathematical Methods in Physics, Community & Population Ecology