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Full Description
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, phys ics, 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 sys tem 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.
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.
