Nonlinear Physics with Maple for Scientists and EngineersPhilosophy 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
Topological Analysis | 4 |
Nonlinear Systems Part I | 35 |
Nonlinear Lattice Dynamics | 47 |
Nonlinear Systems Part II | 77 |
5 | 136 |
Analytic Methods | 165 |
125 | 203 |
163 | 211 |
Compound Pendulum | 549 |
Van der Pol Limit Cycle | 559 |
Drinking Bird | 569 |
Hard Spring | 577 |
Electrical | 585 |
Magnetic | 589 |
Period Doubling | 593 |
Period Doubling | 595 |
Limit Cycles | 261 |
Forced Oscillators | 284 |
Nonlinear Maps | 343 |
Nonlinear PDE Phenomena | 401 |
Numerical Simulation | 437 |
Inverse Scattering Method | 473 |
Introduction to Nonlinear Experiments | 495 |
Driven Eardrum | 503 |
Anharmonic Potential | 511 |
Iron Core Inductor | 517 |
Tunnel Diode Negative Resistance Curve | 527 |
Tunnel Diode SelfExcited Oscillator | 533 |
Focal Point Instability | 543 |
FiveWell Magnetic Potential | 599 |
Power Spectrum | 605 |
Entrainment and Quasiperiodicity | 609 |
Quasiperiodicity | 611 |
Chuas Butterfly | 613 |
Route to Chaos | 617 |
Driven Spin Toy | 621 |
Mapping | 623 |
| 627 | |
| 641 | |
| 648 | |
Other editions - View all
Nonlinear Physics with Maple for Scientists and Engineers Richard H. Enns,George C. McGuire Limited preview - 2012 |
Nonlinear Physics with Maple for Scientists and Engineers Richard Enns,George McGuire Limited preview - 2013 |
Common terms and phrases
3-dimensional airtrack amplitude analytic approximation behavior bifurcation calculate capacitor chaos chaotic Chapter circuit coefficient commands in file Confirm constant cos(wt curve damping derivative determine diffusion equation discussed display dsolve Duffing equation eardrum End Example energy Euler Experimental Activity fixed point force fractal function given glider hard spring Hénon map initial conditions input integral iterations KdV equation limit cycle logistic map Lorenz magnet Maple commands Maple file method negative nonlinear ODE nonlinear systems numerical obtained output parameters period doubling phase plane plot Poincaré section Poincaré-Bendixson theorem potential power spectrum PROBLEMS Problem produce region relaxation oscillations result shown in Figure simple pendulum sine-Gordon equation singular points solitary wave solitary wave solutions solitons solve stable stationary points stepsize strange attractor term theorem trajectory tunnel diode unstable values variable velocity voltage Xn+1 zero