Asymptotic Perturbation Methods: For Nonlinear Differential Equations in Physics

Asymptotic Perturbation Methods is a book that provides a comprehensive overview of powerful mathematical methods to solve differential equations in physics. It focuses on nonlinearity in various fields of physics and presents a unified view on nonlinear systems by offering a common framework to obtain approximate solutions to nonlinear partial differential equations through the asymptotic perturbation method. The book covers applications, including the Maccari method, nonlinear oscillators, limit cycles, iterated nonlinear maps, continuous systems, and nonlinear partial differential equations. It is written by a highly qualified author with significant accomplishments in the field and is ideal for an introductory course at the senior or first-year graduate level, as well as a valuable reference for professional scientists.

Format: Hardback
Length: 256 pages
Publication date: 15 February 2023
Publisher: Wiley-VCH Verlag GmbH

Asymptotic Perturbation Methods: A Comprehensive Overview of Powerful Mathematical Techniques for Solving Differential Equations in Physics

In the realm of physics, the study of nonlinearity is a fundamental aspect that requires intricate mathematical methods to unravel. Asymptotic Perturbation Methods for Nonlinear Differential Equations in Physics emerges as a comprehensive guide, offering a cohesive overview of these powerful mathematical techniques. By delving into the mathematical description of nonlinearity in the form of nonlinear partial differential equations, the book provides a unified perspective on nonlinear systems across diverse fields of physics. Through the application of the asymptotic perturbation method, it offers a framework for obtaining approximate solutions to these complex nonlinear partial differential equations.

One of the remarkable features of this book is its comprehensive coverage of a intricate topic. It encompasses a wide range of topics, including the application of various flavors of the asymptotic perturbation method, such as the Maccari method, to governing equations of nonlinear systems. The book also delves into nonlinear oscillators, limit cycles, and their bifurcations, iterated nonlinear maps, continuous systems, and nonlinear partial differential equations (NPDEs). Furthermore, it explores advanced topics such as nonlinear systems, including the van der Pol oscillator, with comprehensive coverage of plasma physics, quantum mechanics, elementary particle physics, cosmology, and chaotic systems.

In addition to its thoroughness, the book emphasizes applications throughout. Numerous examples are included, elucidating the concepts in a practical and accessible manner. The scientific background is explained at an elementary level, seamlessly integrated with the mathematical theory to enhance reader comprehension. To fully grasp the intricacies within this book, it is essential to possess a solid foundation in multivariable calculus and introductory physics.

Written by a highly qualified author with extensive accomplishments in the field, Asymptotic Perturbation Methods for Nonlinear Differential Equations in Physics offers a valuable resource for students, researchers, and practitioners alike. With its clear and concise writing style, the book provides a solid foundation for understanding the complexities of nonlinearity in physics. Whether you are a physicist seeking to deepen your understanding of nonlinearity or a mathematician interested in exploring new mathematical techniques, this book is an indispensable guide.

Weight: 652g
Dimension: 244 x 170 x 19 (mm)
ISBN-13: 9783527414215