Introduction to Perturbation Methods

1. Front Matter

   Pages i-xiii

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2. Introduction to Asymptotic Approximations

   • Mark H. Holmes

   Pages 1-45

3. Matched Asymptotic Expansions

   • Mark H. Holmes

   Pages 47-104

4. Multiple Scales

   • Mark H. Holmes

   Pages 105-159

5. The WKB and Related Methods

   • Mark H. Holmes

   Pages 161-222

6. The Method of Homogenization

   • Mark H. Holmes

   Pages 223-248

7. Introduction to Bifurcation and Stability

   • Mark H. Holmes

   Pages 249-295

8. Back Matter

   Pages 297-337

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This book is an introductory graduate text dealing with many of the perturbation methods currently used by applied mathematicians, scientists, and engineers. The author has based his book on a graduate course he has taught several times over the last ten years to students in applied mathematics, engineering sciences, and physics. The only prerequisite for the course is a background in differential equations. Each chapter begins with an introductory development involving ordinary differential equations. The book covers traditional topics, such as boundary layers and multiple scales. However, it also contains material arising from current research interest. This includes homogenization, slender body theory, symbolic computing, and discrete equations. One of the more important features of this book is contained in the exercises. Many are derived from problems of up- to-date research and are from a wide range of application areas.

• Perturbation Methods
• applied mathematics
• bifurcation
• convergence
• differential equation
• homogenization
• Hypergeometric function
• integral
• ordinary differential equation
• partial differential equation
• solution
• stability

• Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, USA

  Mark H. Holmes

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