Cambridge Texts in Applied Mathematics: Nonlinear Systems Series Number 10

Cambridge Texts in Applied Mathematics: Nonlinear Systems Series Number 10

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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.
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Product details

  • Paperback | 352 pages
  • 152 x 229 x 20mm | 520g
  • Cambridge, United Kingdom
  • English
  • 2 Plates, color
  • 0521406684
  • 9780521406680
  • 1,658,905

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.
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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 Supplement "This is a volume in the series Cambridge Texts in Applied mathematics. It is an introduction to the theories of bifurcation and chaos. It treats the solution of nonlinear equations, especially difference and ordinary differential equations, as the parameter varies..." Quarterly of Applied Mathematics "...can be used as an effective text to introduce the topics involved with nonlinear dynamics." Subhash C. Sinha, Applied Mechanics Review "...a useful book which contains an abundance of interesting problems and so will be of immense value to anyone planning a course on the subject." Tom Mullin, The Times Higher Education Supplement "...we have not yet seen in the literature any generally accepted textbooks...It seems to me that this book is an honest and praiseworthy attempt to fill precisely this educational gap. In my opinion, it is quite successful in this regard, and its aim to attract and stimulate the curious student of applied sciences is largely fulfilled....well-written and well equipped to serve as a text, from which teachers and students will find much to draw upon in order to improve their working knowledge of nonlinear dynamics and chaos....I highly recommend it." Tassos Bountis, Mathematical Reviews "The strength of this book lies in its examples and exercises. Each topic is illustrated with marvelously detailed examples, and there is a total of 214 exercises with many solutions and hints." Joseph Gruendler, SIAM Review
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