Nonlinear Dynamics: Exploration Through Normal Forms (Dover Books on Physics)

Book Details:

• Author: Peter B. Kahn

• Publisher: Dover

• Binding: Paperback

• Number of Pages: 416

• ISBN-13: 0800759780457

• Languages: English

• Dimensions: 8.9 x 6.0 x 0.9 inches

About The Book:
Normal Forms and Perturbation Analysis of Ordinary Differential Equations by Peter B. Kahn is a comprehensive guide designed for advanced undergraduates and graduate students. The book explores the method of normal forms and its application to ordinary differential equations through perturbation analysis. Perfect for those studying mathematical modeling in science and engineering, this work emphasizes the flexibility of the normal form expansion, showcasing how this approach can be applied to a wide range of problems encountered in various scientific fields.

The text begins with an introduction to the fundamental concepts behind normal forms before delving into systems with one degree of freedom, particularly oscillations where the force has a dominant linear term and a small nonlinear term. It also addresses a range of nonautonomous systems that are common when studying forced oscillatory motion. Key topics covered include boundary value problems, the method of the center manifold, linear and nonlinear Mathieu equations, pendula, Nuclear Magnetic Resonance (NMR), coupled oscillator systems, and much more.

This book serves as both a learning tool for students and a valuable reference for professionals and researchers dealing with differential equations in engineering, physics, and applied mathematics.