A rigorous yet accessible introduction to partial differential equationsupdated in a valuable new edition <strong>Beginning Partial Differential Equations</stro... » 

A rigorous yet accessible introduction to partial differential equationsupdated in a valuable new edition Beginning Partial Differential EquationsSecond Edition provides a comprehensive introduction to partial differentialequations PDEs with a special focus on the significance of characteristicssolutions by Fourier series integrals and transforms properties and physicalinterpretations of solutions and a transition to the modern function spaceapproach to PDEs. With its breadth of coverage this new edition continues topresent a broad introduction to the field while also addressing morespecialized topics and applications. Maintaining the hallmarks of the previousedition the book begins with firstorder linear and quasilinear PDEs and therole of characteristics in the existence and uniqueness of solutions. Canonicalforms are discussed for the linear secondorder equation along with the Cauchyproblem existence and uniqueness of solutions and characteristics as carriersof discontinuities in solutions. Fourier series integrals and transforms arefollowed by their rigorous application to wave and diffusion equations as wellas to Dirichlet and Neumann problems. In addition solutions are viewed throughphysical interpretations of PDEs. The book concludes with a transition to moreadvanced topics including the proof of an existence theorem for the Dirichletproblem and an introduction to distributions. Additional features of the SecondEdition include solutions by both general eigenfunction expansions andnumerical methods. Explicit solutions of Burgers equation the telegraphequation with an asymptotic analysis of the solution and Poissons equationare provided. A historical sketch of the field of PDEs and an extensive sectionwith solutions to selected problems are also included. Beginning PartialDifferential Equations Second Edition is an excellent book for advancedundergraduate and beginning graduatelevel courses in mathematics scienceand engineering. «