Introduction to Perturbation Methods

Mark Holmes has written a number of successful textbooks and is Professor at Rensselaar Polytechnic Institute.

• Preface.- Preface to Second Edition.- Introduction to Asymptotic Approximations.- Matched Asymptotic Expansions.- Multiple Scales.- The WKB and Related Methods.- The Method of Homogenization- Introduction to Bifurcation and Stability.- References.- Index.

From the reviews of the second edition: "The book is composed of 6 chapters with the topics of Introduction to Asymptotic Approximations, Matched Asymptotic Expansions ... Second-Order Difference Equations, and Delay Equations. ... enjoyed reading this book that has a refreshing flavor to perturbation methods. ... The book can be used for both undergraduate and graduate courses in mathematics and physics and also in aerospace, electrical and mechanical engineering areas. Those working in industry will find this book useful in addressing some of the nonlinear problems in real-world situations." (D. Subbaram Naidu, Amazon.com, March, 2013) "This introduction to perturbation methods is a rich, well-written ... textbook. ... Students and their instructors will benefit greatly from this author's evident broad understanding of applied mathematics and mechanics and his uncommon pedagogical abilities and scholarship. ... Holmes's text will be tough to beat for the ambitious and talented." (Robert E. O'Malley, Jr., SIAM Review, Vol. 55 (3), 2013) "This is the second edition of the well-known book widely used by researchers in applied mathematics and physics, engineers, graduate and postgraduate students. Its distinctive feature is that it includes a variety of substantive physically motivated examples on various kinds functional equations and also exercises both in and at the end of every chapter." (Boris V. Loginov, zbMATH, Vol. 1270, 2013)