Applied Partial Differential Equations (3 ed.)
Abstract
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.
Collections
- Sociology [3570]
Related items
Showing items related by title, author, creator and subject.
-
Boundary regularized integral equation formulation of the Helmholtz equation in acoustics
Sun, Qiang; Klaseboer, Evert; Cheong Khoo, Boo (The Royal Society, 2015)A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach ... -
A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations
Islam, Md. Shafiqul; Khan, Kamruzzaman; AKBar, M. Ali (2014)The purpose of this article is to present an analytical method, namely the improvedF-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is ... -
A Short Course in Ordinary Differential Equations
Kong, Qingkai (Springer, 2014)This text is a rigorous treatment of the basic qualitative theory of ordinary differential equations, at the beginning graduate level. Designed as a flexible one-semester course but offering enough material for two semesters, ...