Essential Perturbation Methods

This book presents the modeling and scaling of physical problems, which result in normalized perturbation equations. This is followed by solving perturbation problems and evaluating the results. The author refines perturbation methods into simple, understandable elements and avoids unnecessary theorems and proofs. In addition, the results are consolidated and interpreted, and the presented examples are succinct to illustrate the essential techniques. This book is ideal and beneficial for practicing scientists and engineers who need to understand and apply perturbation methods to difficult problems with applications in mathematics, engineering, and biology. Discussions on new perspectives, simpler presentations on convergence, and the expansion of integrals are included.

Refines perturbation methods into simple, understandable elements for practicing scientists and engineers Models and scales physical problems resulting in normalized perturbation equations Contains practical and necessary tools for using and applying perturbation methods

Auteur
C.Y. Wang, Ph.D., is a Professor in the Department of Mathematics and Adjoint Professor in the Department of Mechanical Engineering at Michigan State University, East Lansing. He received his B.S. from Taiwan University and Ph.D. from the Massachusetts Institute of Technology. Dr. Wang has authored two book and approximately 550 journal articles. He has also served as a technical editor of Applied Mechanics Reviews.

Résumé

"This textbook can be used by undergraduate and graduate students and can also serve as a comprehensive guide for those seeking an understanding of perturbation techniques and their practical applications. ... The author's pedagogical approach, marked by clarity, coherence, and a student-centered perspective, makes this textbook reader friendly and accessible. References to classical texts at the end of each chapter enhance the educational experience, facilitate continuous learning and support students in further exploration of the subject matter." (Svitlana P. Rogovchenko, Mathematical Reviews, May, 2024)

Contenu

Nondimensionalization and scaling.- Asymptotic expansion.- Basic theory.- Eigenvalue problems.- Perturbation of integrals.- The phase plane.- Periodic and almost periodic solutions.- Singular perturbation and boundary layers.- Other singular problems.- Improving asymptotic series.- Examples in mechanics. <p