Perturbation Techniques in Mathematics, Engineering & Physics - Brossura

Bellman, Richard Ernest

Brossura

ISBN 10: 0486432580 ISBN 13: 9780486432588

Casa editrice: Dover Pubns, 2003

Riassunto

An introduction to a variety of perturbation techniques for ordinary differential equations, this work outlines applications through specific examples. Mathematicians, engineers, and applied scientists will find its exposition entirely accessible.
The first part covers the classical perturbation techniques. Dr. Bellman begins with a readily solved linear algebraic equation that exhibits some of the versatility of the Lagrange expansion theorem. This leads by easy stages to a discussion of the matrix exponential and to a brief excursion into the domain of Poincaré   and Lyapunov, where invariant imbedding is illustrated. Subsequent discussions of alternative perturbation techniques employ dynamic programming. The second chapter concentrates on nonlinear differential equations, presenting renormalization techniques of Lindstedt and Shohat and averaging techniques by Bellman and Richardson. The concluding chapter considers a variety of questions centering on a second-order linear differential equation, explaining the applications of the WKB-Liouville method and asymptotic series.
Exercises, comments, and an annotated bibliography follow each demonstration of technique. The text presupposes a course in intermediate calculus and rudiments of the theory of ordinary differential equations. For the engineer, physicist, or mathematician working in fields requiring the solution of differential equations, this text provides a stimulating introduction to analytical approximation techniques.

Su questo libro

Product Description:

Graduate students receive a stimulating introduction to analytical approximation techniques for solving differential equations in this text, which introduces a series of interesting and scientifically significant problems, indicates useful solutions, and supplies a guide to further reading. Intermediate calculus and basic grasp of ordinary differential equations are prerequisites. 1966 edition.

Contenuti:

1. Classical Perturbation Techniques 2. Periodic Solutions of Nonlinear Differential Equations and Renormalization Techniques 3. The Liouville-WKB Approximation and Asymptotic Series Subject Index. Author Index

Su questa edizione

• Editore: Dover Pubns
• Data di pubblicazione: 2003
• ISBN 10: 0486432580
• ISBN 13: 9780486432588
• Rilegatura: Copertina flessibile
• Numero di pagine: 128