Perturbation techniques with the emphasis on developing asymptotic solutions: approximation of integrals Laplace's method, stationary phase method, method of steepest descent , regular perturbations of ODEs, singular perturbations to ODEs matched asymptotic expansions, WKB approximation , multiple scale methods. For most equations that arise in modeling applications it is unlikely that exact solutions can be found. Even convergent series approximations are often not available, or they are of limited use if they converge very slowly. Instead, asymptotic expansions can yield good approximations. They are typically divergent if summed to infinity but a few terms can often give excellent and well defined approximations. This course will introduce the basic ideas and show how they can be applied to algebraic and differential equations, and to the evaluation of integrals.
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Return to Book Page. Preview — Perturbation Methods by E. Perturbation Methods by E. In this book the author presents the theory and techniques underlying perturbation methods in a manner that will make the book widely appealing to readers in a broad range of disciplines. Methods of algebraic equations, asymptotic expansions, integrals, PDEs, strained coordinates, and multiple scales are illustrated by copious use of examples drawn from many areas of mathe In this book the author presents the theory and techniques underlying perturbation methods in a manner that will make the book widely appealing to readers in a broad range of disciplines.
Methods of algebraic equations, asymptotic expansions, integrals, PDEs, strained coordinates, and multiple scales are illustrated by copious use of examples drawn from many areas of mathematics and physics. The philosophy adopted is that there is no single or best method for such problems, but that one may exploit the small parameter given some experience and understanding of similar perturbation problems.
The author does not look to perturbation methods to give quantitative answers but rather uses them to give a physical understanding of the subtle balances in a complex problem.
Get A Copy. Paperback , pages. Published October 25th by Cambridge University Press. More Details Other Editions 3. Friend Reviews. To see what your friends thought of this book, please sign up. To ask other readers questions about Perturbation Methods , please sign up.
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Asymptotic and Perturbation Methods
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