Nonlinear Systems

Nonlinear Systems

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Description

The theories of bifurcation, chaos and fractals as well as equilibrium, stability and nonlinear oscillations, are part of the theory of the evolution of solutions of nonlinear equations. A wide range of mathematical tools and ideas are drawn together in the study of these solutions, and the results applied to diverse and countless problems in the natural and social sciences, even philosophy. The text evolves from courses given by the author in the UK and the United States. It introduces the mathematical properties of nonlinear systems, mostly difference and differential equations, as an integrated theory, rather than presenting isolated fashionable topics. Topics are discussed in as concrete a way as possible and worked examples and problems are used to explain, motivate and illustrate the general principles. The essence of these principles, rather than proof or rigour, is emphasized. More advanced parts of the text are denoted by asterisks, and the mathematical prerequisites are limited to knowledge of linear algebra and advanced calculus, thus making it ideally suited to both senior undergraduates and postgraduates from physics, engineering, chemistry, meteorology etc. as well as mathematics.show more

Product details

  • Online resource
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • English
  • 2 colour illus.
  • 113917245X
  • 9781139172455

Review quote

' ... contains an abundance of interesting problems ... will be of immense value to anyone planning a course on the subject.' The Times Higher Education Supplementshow more

Table of contents

1. Introduction; 2. Classification of bifurcations of equilibrium solutions; 3. Difference equations; 4. Some special topics; 5. Ordinary differential equations; 6. Second-order autonomous ordinary differential systems; 7. Forced oscillations; 8. Chaos; Bibliography; Index.show more