Partial Differential Equations

Undergraduate courses on partial differential equations (PDEs) have traditionally been based on the Fourier series method for analysing and solving PDEs. What this textbook offers is a fresh approach; the traditional method taught alongside the modern finite element method. Both powerful methods are introduced to the reader and emphasised equally. A further beneficial feature of the book is that it uses the language of linear algebra, in particular in emphasising the role of best approximation in function spaces and the idea of an eigenfunction expansion. Its inclusion of realistic physical experiments for many examples and exercises will make the book appealing to science and engineering students, as well as students of mathematics. This second edition has a broader coverage of PDE methods and applications than the first, with the inclusion of chapters on the method of characteristics, Green's functions, Sturm–Liouville problems and a section on finite difference methods.

Mark Gockenbach is Professor and Chair of the Department of Mathematical Sciences at Michigan Technological University. He is the author of Partial Differential Equations: Analytical and Numerical Methods (SIAM, 2002) and Understanding and Implementing the Finite Element Method (SIAM, 2006). His research interests include inverse problems in partial differential equations and numerical methods and software for large-scale optimization problems.