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It's a Nonlinear World / by Richard H. Enns
Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Springer Undergraduate Texts in Mathematics and Technology | SpringerLink BücherPublisher: New York, NY : Springer Science+Business Media, LLC, 2011Edition: 1Description: Online-Ressource (XII, 384p. 145 illus., 8 illus. in color, digital)ISBN:- 9780387753409
- 519
- T57-57.97
- QA3
Contents:
Summary: Preface -- Part I. World of Mathematics -- 1. World of Nonlinear Systems -- 2. World of Nonlinear ODEs -- 3. World of Nonlinear Maps -- 4. World of Solitons -- Part II. Our Nonlinear World -- 5. World of Motion -- 6. World of Sports -- 7. World of Electromagnetism -- 8. World of Weather Prediction -- 9. World of Chemistry -- 10. World of Disease -- 11. World of War -- Bibliography -- Index.Summary: Drawing examples from mathematics, physics, chemistry, biology, engineering, economics, medicine, politics, and sports, this book illustrates how nonlinear dynamics plays a vital role in our world. Examples cover a wide range from the spread and possible control of communicable diseases, to the lack of predictability in long-range weather forecasting, to competition between political groups and nations. After an introductory chapter that explores what it means to be nonlinear, the remainder of Part I covers nonlinear mathematical concepts such as fixed points, limit cycles, fractals, chaos, bifurcations, and solitons, and nonlinear diagnostic tools such as fixed point analysis, bifurcation diagrams, and Lyapunov exponents, to name a few. Part II of the text presents illustrative examples of nonlinear dynamics that are highly relevant to the contemporary world. At the end of each chapter, a wide variety of problems are presented which extend the ideas developed in the chapter as well as allow the reader to explore other aspects of our nonlinear world. The mathematical level of the text assumes good working knowledge of basic calculus and prior exposure to ordinary differential equations and the wave and diffusion equations. The book may be used at the undergraduate or graduate level to prepare science and engineering students for problems in the "real world" or for self-study by practicing scientists and engineers. The more casual reader can simply read the book for intellectual enjoyment.PPN: PPN: 1650435037Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
""Contents""; ""Preface""; ""Part I""; ""Chapter 1""; ""World of Nonlinear Systems""; ""1.1 Introduction to Nonlinear ODE Models""; ""1.2 Introduction to Difference Equation Models""; ""1.3 Solving Nonlinear ODEs on the Computer""; ""Chapter 2""; ""World of Nonlinear ODEs""; ""2.1 Breakdown of Linear Superposition""; ""2.2 Some Analytically Solvable Examples""; ""2.3 Fixed Points and Phase-Plane Analysis""; ""2.4 Bifurcations""; ""2.5 Hysteresis and the Jump Phenomena""; ""2.6 Limit Cycles""; ""2. 7 Strange Attractors and Chaos""; ""2.8 Fractal Dimensions""; ""2.9 Poincare Sections""
""2.10 Pow-er Spectrum""""Chapter 3""; ""World of Nonlinear Maps""; ""3.1 Fixed Points of One-Dimensional Maps""; ""3.2 Stability Criterion""; ""3.3 Cobweb Diagram""; ""3.4 Period Doubling to Chaos""; ""3.5 Creating Lorenz Maps""; ""3.6 Lyapunov Exponent""; ""3.7 Two-Dimensional Maps""; ""3.8 Mandelbrot and Julia Sets""; ""3.9 Chaos versus Noise""; ""3.10 Controlling Chaos""; ""Chapter 4""; ""World of Solitons""; ""4.1 Korteweg-rieVries Solitons""; ""4.2 Sine-Gordon Solitons""; ""4.3 Similarity Solutions""; ""4.4 Numerical Simulation""; ""4.4.1 Finite Difference Approximations""
""4.4.2 The Zabusky-Kruskal Algorithm""""4.4.3 Method of Characteristics""; ""4.4.4 Numerical Algorithm for the SGE""; ""4.4.5 Numerical Stability""; ""4.5 Extension to Cellular Automata""; ""Part II""; ""Chapter 5""; ""World of Motion""; ""5.1 Nonlinear Drag or Resistance""; ""5.2 Nonlinear Lift""; ""5.3 The Pendulum, Simple and Otherwise""; ""5.3.1 The Simple Pendulum""; ""5.3.2 Parametric Excitation""; ""5.3.3 The Rotating Pendulum""; ""5.4 Nonlinear Springs""; ""5.4.1 Lattice Dynamics""; ""5.5 Hysteresis and Jumps Revisited""; ""5.6 Precession of Mercury""
""5.7 Saturn's Rings: A ""Toy"" Model""""5.8 Hamiltonian Chaos""; ""Chapter 6""; ""World of Sports""; ""6.1 The Aerodynamics of Sports Balls""; ""6.2 Bend It Like Beckham""; ""6.3 A Major League Curveball""; ""6.4 Golf Ball Trajectory""; ""6.5 A Falling Badminton Bird""; ""6.6 Car Racing""; ""6. 7 Medieval Archery""; ""Chapter 7""; ""World of Electromagnetism""; ""7.1 Nonlinear Electrical Circuits""; ""7.1.1 Nonlinear Inductance""; ""7.1.2 Nonlinear Capacitance""; ""7.1.3 Chua's Circuit: Piecewise-Linear Negative Resistance""; ""7.1.4 Tunnel Diode Oscillator""; ""7.1.5 Josephson Junction""
""7.1.6 SQUID Magnetometer""""7.2 Nonlinear Optics""; ""7.2.1 Optical Soliton Propagation""; ""7.2.2 The Navier-Stokes Equations""; ""7.2.3 Stimulated Scattering of Light""; ""7.3 The Earth's Magnetic Field""; ""7.3.1 Aurora Borealis""; ""7.3.2 The Drifting North Magnetic Pole""; ""7.3.3 The Geodynamo Origin of the Earth's Magnetic Field""; ""Chapter 8""; ""World of Weather Prediction""; ""8.1 Early History""; ""8.2 The Barotropic Vorticity Equation""; ""8.3 SOIIle Meteorological Concepts""; ""8.4 Modern Numerical Weather Forecasting""; ""Chapter 9""; ""World of Chemistry""
""9.1 Chemical Reactions""
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