Applied Partial Differential Equations

A vibrant field of study, partial differential equations arise in mathematical models whose dependent variables change continuously as functions of several independent variables (often space and time). Their power lies in their universality: there is a huge and ever-growing range of real-world problems to which they can be applied, from fluid mechanics and electromagnetism to probability and finance. This book is a lively and well-written guide to both the theory and applications of PDEs. It examines such questions as the well-posedness of a PDE problem and the conditions under which solutions change little with small changes in input. It also examines the problem of establishing the accuracy of a numerical solution to a PDE, an increasingly important question given the power of new numerical methods and software.