Ebook: Nonlinear Physics with Mathematica for Scientists and Engineers

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.

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Content:
Front Matter....Pages i-xv
Front Matter....Pages 1-2
Introduction....Pages 3-38
Nonlinear Systems. Part I....Pages 39-80
Nonlinear Systems. Part II....Pages 81-124
Topological Analysis....Pages 125-166
Analytic Methods....Pages 167-222
The Numerical Approach....Pages 223-264
Limit Cycles....Pages 265-292
Forced Oscillators....Pages 293-354
Nonlinear Maps....Pages 355-412
Nonlinear PDE Phenomena....Pages 413-450
Numerical Simulation....Pages 451-490
Inverse Scattering Method....Pages 491-510
Front Matter....Pages 511-512
Introduction to Nonlinear Experiments....Pages 513-516
Magnetic Force....Pages 517-520
Magnetic Tower....Pages 521-524
Spin Toy Pendulum....Pages 525-528
Driven Eardrum....Pages 529-532
Nonlinear Damping....Pages 533-536
Anharmonic Potential....Pages 537-542
Iron Core Inductor....Pages 543-546
Front Matter....Pages 511-512
Nonlinear LRC Circuit....Pages 547-552
Tunnel Diode Negative Resistance Curve....Pages 553-558
Tunnel Diode Self-Excited Oscillator....Pages 559-562
Forced Duffing Equation....Pages 563-568
Focal Point Instability....Pages 569-574
Compound Pendulum....Pages 575-576
Damped Simple Pendulum....Pages 577-578
Stable Limit Cycle....Pages 579-586
Van der Pol Limit Cycle....Pages 587-590
Relaxation Oscillations: Neon Bulb....Pages 591-596
Relaxation Oscillations: Drinking Bird....Pages 597-600
Relaxation Oscillations: Tunnel Diode....Pages 601-604
Hard Spring....Pages 605-608
Nonlinear Resonance Curve: Mechanical....Pages 609-612
Nonlinear Resonance Curve: Electrical....Pages 613-616
Nonlinear Resonance Curve: Magnetic....Pages 617-620
Subharmonic Response: Period Doubling....Pages 621-622
Diode: Period Doubling....Pages 623-626
Five-Well Magnetic Potential....Pages 627-632
Power Spectrum....Pages 633-636
Front Matter....Pages 511-512
Entrainment and Quasiperiodicity....Pages 637-638
Quasiperiodicity....Pages 639-640
Chua’s Butterfly....Pages 641-644
Route to Chaos....Pages 645-648
Driven Spin Toy....Pages 649-650
Mapping....Pages 651-653
Back Matter....Pages 655-695

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Content:
Front Matter....Pages i-xv
Front Matter....Pages 1-2
Introduction....Pages 3-38
Nonlinear Systems. Part I....Pages 39-80
Nonlinear Systems. Part II....Pages 81-124
Topological Analysis....Pages 125-166
Analytic Methods....Pages 167-222
The Numerical Approach....Pages 223-264
Limit Cycles....Pages 265-292
Forced Oscillators....Pages 293-354
Nonlinear Maps....Pages 355-412
Nonlinear PDE Phenomena....Pages 413-450
Numerical Simulation....Pages 451-490
Inverse Scattering Method....Pages 491-510
Front Matter....Pages 511-512
Introduction to Nonlinear Experiments....Pages 513-516
Magnetic Force....Pages 517-520
Magnetic Tower....Pages 521-524
Spin Toy Pendulum....Pages 525-528
Driven Eardrum....Pages 529-532
Nonlinear Damping....Pages 533-536
Anharmonic Potential....Pages 537-542
Iron Core Inductor....Pages 543-546
Front Matter....Pages 511-512
Nonlinear LRC Circuit....Pages 547-552
Tunnel Diode Negative Resistance Curve....Pages 553-558
Tunnel Diode Self-Excited Oscillator....Pages 559-562
Forced Duffing Equation....Pages 563-568
Focal Point Instability....Pages 569-574
Compound Pendulum....Pages 575-576
Damped Simple Pendulum....Pages 577-578
Stable Limit Cycle....Pages 579-586
Van der Pol Limit Cycle....Pages 587-590
Relaxation Oscillations: Neon Bulb....Pages 591-596
Relaxation Oscillations: Drinking Bird....Pages 597-600
Relaxation Oscillations: Tunnel Diode....Pages 601-604
Hard Spring....Pages 605-608
Nonlinear Resonance Curve: Mechanical....Pages 609-612
Nonlinear Resonance Curve: Electrical....Pages 613-616
Nonlinear Resonance Curve: Magnetic....Pages 617-620
Subharmonic Response: Period Doubling....Pages 621-622
Diode: Period Doubling....Pages 623-626
Five-Well Magnetic Potential....Pages 627-632
Power Spectrum....Pages 633-636
Front Matter....Pages 511-512
Entrainment and Quasiperiodicity....Pages 637-638
Quasiperiodicity....Pages 639-640
Chua’s Butterfly....Pages 641-644
Route to Chaos....Pages 645-648
Driven Spin Toy....Pages 649-650
Mapping....Pages 651-653
Back Matter....Pages 655-695
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