Applied Partial Differential Equations: An Introduction

Jeffrey provides a modern, useful introduction to Partial Differential Equations with an emphasis on using the theory to solve current, real problems. Various applications leading to linear elliptic, parabolic and hyperbolic equations are considered in detail, together with the important effects of nonlinearity in the case of hyperbolic equations and systems.Foremost amongst the intriguing physical examples of the effects of nonlinearity in the hyperbolic case is how abrupt changes in pressure produced ahead of an aircraft in supersonic flight creates a shock wave, which is experienced by an observer on the ground as a sonic boom. Analogous phenomena are found in the study of water waves where hydraulic jumps can occur, in solids where shock waves can develop, in chromatography where an abrupt change in color or concentration occurs across an interface in fluid, and in many other practical situations.Applied Partial Differential Equations is a contemporary and valuable resource for aspiring and working engineers, applied mathematicians and scientists.I like the topics covered, the inclusion of conservation laws and physical principles, and the inclusion of homework solutions better than any text I can think of. - William F. Moss, Clemson University"