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Enns R.H., McGuire G.С. Nonlinear Physics with Mathematica for Scientists and Engineers

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Enns R.H., McGuire G.С. Nonlinear Physics with Mathematica for Scientists and Engineers
Birkhauser, Boston, Berlin, 2001, 725 pp.
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 a powerful computer algebra software system applied to examples from these disciplines.
Contents.
Preface.
I - Theory.
Introduction.
Nonlinear Systems. Part I.
Nonlinear Systems. Part II.
Topological Analysis.
Analytic Methods.
The Numerical Approach.
Limit Cycles.
Forced Oscillators.
Nonlinear Maps.
Nonlinear PDE Phenomena.
Numerical Simulation.
Inverse Scattering Method.
II - Experimental activities.
Introduction to Nonlinear Experiments.
Magnetic Force.
Magnetic Tower.
Spin Toy Pendulum.
Driven Eardrum.
Nonlinear Damping.
Anharmonic Potential.
Iron Core Inductor.
Nonlinear LRC Circuit.
Tunnel Diode Negative Resistance Curve.
Tunnel Diode Self-Excited Oscillator.
Forced Duffing Equation.
Focal Point Instability.
Compound Pendulum.
Damped Simple Pendulum.
Stable Limit Cycle.
Van der Pol Limit Cycle.
Relaxation Oscillations: Neon Bulb.
Relaxation Oscillations: Drinking Bird.
Relaxation Oscillations: Tunnel Diode.
Hard Spring.
Nonlinear Resonance Curve: Mechanical.
Nonlinear Resonance Curve: Electrical.
Nonlinear Resonance Curve: Magnetic.
Subharmonic Response: Period Doubling.
Diode: Period Doubling.
Five-Well Magnetic Potential.
Power Spectrum.
Entrainment and Quasiperiodicity.
Quasiperiodicity.
Chua's Butterfly.
Route to Chaos.
Driven Spin Toy.
Mapping.
Bibliography.
Index.
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