Applied Partial Differential Equations

Abstract

The goal of this new edition is the same as that for the original, namely, to present a one-semester treatment of the basic ideas encountered in partial differential equations (PDEs). The text is designed for a 3-credit semester course for undergraduate students in mathematics, science, and engineering. The prerequisites are calculus and ordinary differential equations. The text is intimately tied to applications in heat conduction, wave motion, biological systems, and a variety other topics in pure and applied science. Therefore, students should have some interest, or experience, in basic science or engineering. The main part of the text is the first four chapters, which cover the essential concepts. Specifically, they treat first- and second-order equations on bounded and unbounded domains and include transform methods (Laplace and Fourier), characteristic methods, and eigenfunction expansions (separation of variables); there is considerable material on the origin of PDEs in the natural sciences and engineering. Two additional chapters, Chapter 5 and Chapter 6, are short introductions to applications of PDEs in biology and to numerical computation of solutions. The text offers flexibility to instructors who, for example, may want to insert topics from biology or numerical methods at any time in the course. A brief appendix reviews techniques from ordinary differential equations. Sections marked with an asterisk (*) may safely be omitted. The mathematical ideas are strongly motivated by physical problems, and the exposition is presented in a concise style accessible to students in science and engineering. The emphasis is on motivation, methods, concepts, and interpretation rather than formal theory.