Nonlinear Physics with Mathematica for Scientists and Engineers, 2001

Nonlinear physics continues to be an area of dynamic modern research, with applications to physics, engineering, chemistry, mathematics, computer science, biology, medicine and economics. In this text extensive use is made of the Mathematica computer algebra system. No prior knowledge of Mathematica or programming is assumed. This book includes 33 experimental activities that are designed to deepen and broaden the reader's understanding of nonlinear physics. These activities are correlated with Part I, the theoretical framework of the text.

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 Magnetic Force.- 2 Magnetic Tower.- 3 Spin Toy Pendulum.- 4 Driven Eardrum.- 5 Nonlinear Damping.- 6 Anharmonic Potential.- 7 Iron Core Inductor.- 8 Nonlinear LRC Circuit.- 9 Tunnel Diode Negative Resistance Curve.- 10 Tunnel Diode Self-Excited Oscillator.- 11 Forced Duffing Equation.- 12 Focal Point Instability.- 13 Compound Pendulum.- 14 Damped Simple Pendulum.- 15 Stable Limit Cycle.- 16 Van der Pol Limit Cycle.- 17 Relaxation Oscillations: Neon Bulb.- 18 Relaxation Oscillations: Drinking Bird.- 19 Relaxation Oscillations: Tunnel Diode.- 20 Hard Spring.- 21 Nonlinear Resonance Curve: Mechanical.- 22 Nonlinear Resonance Curve: Electrical.- 23 Nonlinear Resonance Curve: Magnetic.- 24 Subharmonic Response: Period Doubling.- 25 Diode: Period Doubling.- 26 Five-Well Magnetic Potential.- 27 Power Spectrum.- 28 Entrainment and Quasiperiodicity.- 29 Quasiperiodicity.- 30 Chua’s Butterfly.- 31 Route to Chaos.- 32 Driven Spin Toy.- 33 Mapping.