Wavefronts and Rays as Characteristics and Asymptotics

Characteristics and asymptotics of partial differential equations play an important role in mathematical physics since they lead to insightful solutions of complex problems that might not be solvable otherwise. They constitute, however, a difficult subject, and the purpose of this book, with its additions and refinements that led to its third edition, is to present this subject in an accessible manner, without decreasing the rigor. As any method, characteristics and asymptotics have their limitations. This important issue is addressed in the last chapter, where we discuss caustics, which must be understood in applications of the method, and which constitute a fertile ground for further mathematical research.The book is both a research reference and a textbook. Its careful and explanatory style, which includes numerous exercises with detailed solutions, makes it an excellent textbook for senior undergraduate and graduate courses, as well as for independent studies. Six appendices are provided, which form a self-contained course on applied mathematics and can be used as a textbook on its own.Contents: Characteristic Equations of First-Order Linear Partial Differential EquationsCharacteristic Equations of Second-Order Linear Partial Differential EquationsCharacteristic Equations of First-Order Nonlinear Partial Differential EquationsPropagation of Discontinuities for Linear Partial Differential EquationsCausticsAfterwordAppendices:Integral TheoremsElastodynamic EquationsMaxwell Equations In VacuoFourier Series and TransformsDistributionsGreen's Functions
Readership: Students and researchers in continuum mechanics and mathematical physics.Characteristic Equation;Asymptotic Equation;Partial Differential Equation;Waves0Key Features:The book is a carefully formulated document, whose clarity has been commented on by many readers and lecturersThe book contains many problems whose detailed solutions allow for a self study as well as a verification of understanding of the materialThe book is a result of many research collaborations with distinguished scientists. This is apparent within the book itself and in a selectively chosen references for a further enquiry