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.

List 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 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.

Summary

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.

Additional text

"This book is a revision of an earlier work that looked at nonlinear physics using MAPLE® software. As with that work, Enns and McGuire incorporate theory, experiment, and numerical applications in a thorough introduction to a wide range of nonlinear topics. … The book assumes no familiarity with nonlinear physics or MATHEMATICA® . . . The authors do an extraordinary job of integrating application and theory. They provide applications from a variety of disciplines throughout the sections that introduce the theory and that look at methods of analysis and consider the various approaches to addressing nonlinear problems. It is not an exaggeration to say that this book considers all areas of interest in nonlinear analysis with solid introductions. (This reviewer, having taught the basics of nonlinear physics over the last 15 years, wishes he had had this book as a tutor.) Added to this are 33 experimental activities using MATHEMATICA® that demonstrate concepts and applied examples."
—Choice
Reviewer comments on the Maple edition of NONLINEAR PHYSICS:
"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
"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 in Physics
"...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'sstrength 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,...software, and lab manual gives the newcomer to nonlinear physics quite an effective set of tools.... Basic ideas are explained clearly and illustrated with many examples."
-Physics Today
"... 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

Report

"This book is a revision of an earlier work that looked at nonlinear physics using MAPLE® software. As with that work, Enns and McGuire incorporate theory, experiment, and numerical applications in a thorough introduction to a wide range of nonlinear topics. ... The book assumes no familiarity with nonlinear physics or MATHEMATICA® . . . The authors do an extraordinary job of integrating application and theory. They provide applications from a variety of disciplines throughout the sections that introduce the theory and that look at methods of analysis and consider the various approaches to addressing nonlinear problems. It is not an exaggeration to say that this book considers all areas of interest in nonlinear analysis with solid introductions. (This reviewer, having taught the basics of nonlinear physics over the last 15 years, wishes he had had this book as a tutor.) Added to this are 33 experimental activities using MATHEMATICA® that demonstrate concepts and applied examples."
-Choice
Reviewer comments on the Maple edition of NONLINEAR PHYSICS:
"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
"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 in Physics
"...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'sstrength 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,...software, and lab manual gives the newcomer to nonlinear physics quite an effective set of tools.... Basic ideas are explained clearly and illustrated with many examples."
-Physics Today
"... 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

Product details

• Authors: Richard Enns, Richard H Enns, Richard H. Enns, George C McGuire, George C. McGuire
• Publisher: Springer, Basel
• Languages: English
• Product format: Paperback / Softback
• Released: 07.11.2013
• EAN: 9781461266648
• ISBN: 978-1-4612-6664-8
• No. of pages: 695
• Dimensions: 178 mm x 254 mm x 34 mm
• Weight: 1314 g
• Illustrations: XV, 695 p.
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; C, Computer-Aided Design (CAD), Dynamics, Physics, Mathematics and Statistics, Theoretical, Mathematical and Computational Physics, Physics and Astronomy, Physics, general, Mathematical physics, Mathematical & statistical software, Dynamical Systems and Ergodic Theory, Ergodic theory, Dynamical systems, Numerical and Computational Physics, Simulation, Mathematical Software, Computer software, Computer-Aided Engineering (CAD, CAE) and Design, Computer-aided engineering