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This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as boundary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas.
One hundred new pages added including new material on transcedentally small terms, Kummer's function, weakly coupled oscillators and wave interactions.
List of contents
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.
About the author
Mark Holmes is a Professor at Rensselaer Polytechnic Institute, and is currently the Director of the Center for Modeling, Optimization and Computational Analysis. His research interests involve problems integrating modeling and computational analysis. Professor Holmes has three published books in Springer's Texts in Applied Mathematics series: Introduction to Perturbation Methods, Introduction to the Foundations of Applied Mathematics, and Introduction to Numerical Methods in Differential Equations.
Summary
This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as boundary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas.
One hundred new pages added including new material on transcedentally small terms, Kummer's function, weakly coupled oscillators and wave interactions.
Additional text
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)
Report
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)
