Introduction to partial differential equations / Yehuda Pinchover and Jacob Rubinstein.

Includes bibliographical references (p. 364-365) and index.

1. Introduction; 2. First-order equations; 3. Second-order linear equations; 4. The 1D wave equation; 5. Separation of variables; 6. Sturm-Liouville problem; 7. Elliptic equations; 8. Green's function and integral representation; 9. Equations in high dimensions; 10. Variational methods; 11. Numerical methods; 12. Solutions of odd-numbered problems.

A complete introduction to partial differential equations, this textbook provides a rigorous yet accessible guide to students in mathematics, physics, and engineering. The presentation is lively and up to date, paying particular emphasis to developing an appreciation of underlying mathematical theory. Beginning with basic definitions, properties, and derivations of some basic equations of mathematical physics from basic principles, the book studies first order equations, classification of second order equations, and the one-dimensional wave equation. Two chapters are devoted to the separation of variable, whilst others concentrate on a wide range of topics including elliptic theory, Green's functions, variational and numerical methods. A rich collection of worked examples and exercises accompany the text, along with a large number of illustrations and graphs to provide insight into the numerical examples.Solutions to selected exercises are included for students and extended solution sets are available to lecturers from [email protected].