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 variables, 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.

• Many worked examples and exercises, with extended solutions available for lecturers from [email protected]
• An undergraduate textbook which bridges the gap between introductory and advanced courses on differential equations
• Designed for students with a range of abilities

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.