Nonlinear Physics with Maple for Scientists and Engineers / Edition 2

by Richard H. Enns, George C. McGuire

Overview

Philosophy of the Text This text presents an introductory survey of the basic concepts and applied mathematical methods of nonlinear science as well as an introduction to some simple related nonlinear experimental activities. Students in engineering, physics, chemistry, mathematics, computing science, and biology should be able to successfully use this book. In an effort to provide the reader with a cutting edge approach to one of the most dynamic, often subtle, complex, and still rapidly evolving, areas of modern research-nonlinear physics-we have made extensive use of the symbolic, numeric, and plotting capabilities of the Maple software system applied to examples from these disciplines. No prior knowledge of Maple or computer programming is assumed, the reader being gently introduced to Maple as an auxiliary tool as the concepts of nonlinear science are developed. The CD-ROM provided with this book gives a wide variety of illustrative non­ linear examples solved with Maple. In addition, numerous annotated examples are sprinkled throughout the text and also placed on the CD. An accompanying set of experimental activities keyed to the theory developed in Part I of the book is given in Part II. These activities allow the student the option of "hands on" experience in exploring nonlinear phenomena in the REAL world. Although the experiments are easy to perform, they give rise to experimental and theoretical complexities which are not to be underestimated.

Product Details

ISBN-13:	9781461270935
Publisher:	Birkhäuser Boston
Publication date:	04/19/2013
Edition description:	2nd ed. 2000. Softcover reprint of the original 2nd ed. 2000
Pages:	661
Product dimensions:	7.01(w) x 10.00(h) x 0.05(d)

Table of Contents

I Theory.- 1 Introduction.- 2 Nonlinear Systems. Part I.- 3 Nonlinear Systems. Part II.- 4 Topological Analysis.- 5 Analytic Methods.- 6 The Numerical Approach.- 7 Limit Cycles.- 8 Forced Oscillators.- 9 Nonlinear Maps.- 10 Nonlinear PDE Phenomena.- 11 Numerical Simulation.- 12 Inverse Scattering Method.- II Experimental Activities.- to Nonlinear Experiments.- 1 Spin Toy Pendulum.- 2 Driven Eardrum.- 3 Nonlinear Damping.- 4 Anharmonic Potential.- 5 Iron Core Inductor.- 6 Nonlinear LRC Circuit.- 7 Tunnel Diode Negative Resistance Curve.- 8 Tunnel Diode Self-Excited Oscillator.- 9 Forced Duffing Equation.- 10 Focal Point Instability.- 11 Compound Pendulum.- 12 Stable Limit Cycle.- 13 Van der Pol Limit Cycle.- 14 Relaxation Oscillations: Neon Bulb.- 15 Relaxation Oscillations: Drinking Bird.- 16 Relaxation Oscillations: Tunnel Diode.- 17 Hard Spring.- 18 Nonlinear Resonance Curve: Mechanical.- 19 Nonlinear Resonance Curve: Electrical.- 20 Nonlinear Resonance Curve: Magnetic.- 21 Subharmonic Response: Period Doubling.- 22 Diode: Period Doubling.- 23 Five-Well Magnetic Potential.- 24 Power Spectrum.- 25 Entrainment and Quasiperiodicity.- 26 Quasiperiodicity.- 27 Chua’s Butterfly.- 28 Route to Chaos.- 29 Driven Spin Toy.- 30 Mapping.

Editorial Reviews

"In this second edition extensive use is made of the computer algebra system, Maple® V. No prior knowledge of Maple® or of programming is assumed."

-Zentralblatt Math

"Correctly balances a good treatment of nonlinear, but also nonchaotic, behavior of systems with some of the exciting findings about chaotic dynamics... One of the book’s strengths is the diverse selection of examples from mechanical, chemical, electronic, fluid and many other systems... Another strength of the book is the diversity of approaches that the student is encouraged to take...the authors have chosen well and the trio of text, MAPLE-based software, and the lab manual gives the newcomer to nonlinear physics quite an effective set of tools...this text simultaneously serves as an excellent, structured introduction to MAPLE V...Basic ideas are explained clearly and illustrated with many examples."

-Physics Today (on the first edition)

"The care that the authors have taken to ensure that their text is as comprehensive, versatile, interactive, and student-friendly as possible place this book far above the average."

- Scientific Computing World

"An...excellent book...the authors have been able to cover an extraordinary range of topics and hopefully excite a wide audience to investigate nonlinear phenomena...accessible to advanced undergraduates and yet challenging enough for graduate students and working scientists....The reader is guided through it all with sound advice and humor....I hope that many will adopt the text."

- American Journal of Physics (on the first edition)

"Its organization of subject matter, clarity of writing, and smooth integration of analytic and computational techniques put it among the very best...Richard Enns and George McGuire have written an excellent text for introductory nonlinear physics."

- Computers inPhysics (on the first edition)

From the Publisher