For students with a background in elementary algebra, this book provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia Sets and the Mandelbrot Set, power laws, and cellular automata. The book includes over 200 end-of-chapter exercises.
For students with a background in elementary algebra, this book provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia Sets and the Mandelbrot Set, power laws, and cellular automata. The book includes over 200 end-of-chapter exercises.
David Feldman joined the faculty at College of the Atlantic in 1998, having completed a PhD in Physics at the University of California. He served as Associate Dean for Academic Affairs from 2003 - 2007. At COA Feldman has taught over twenty different courses in physics, mathematics, and computer science. Feldman's research interests lie in the fields of statistical mechanics and nonlinear dynamics. In his research, he uses both analytic and computational techniques. Feldman has authored research papers in journals including Physical Review E, Chaos, and Advances in Complex Systems. In 2011-12 he was a U.S. Fulbright Lecturer in Kigali, Rwanda.
Inhaltsangabe
I. Introducing Discrete Dynamical Systems 0: Opening Remarks 1: Functions 2: Iterating Functions 3: Qualitative Dynamics 4: Time Series Plots 5: Graphical Iteration 6: Iterating Linear Functions 7: Population Models 8: Newton, Laplace, and Determinism II. Chaos 9: Chaos and the Logistic Equation 10: The Buttery Effect 11: The Bifurcation Diagram 12: Universality 13: Statistical Stability of Chaos 14: Determinism, Randomness, and Nonlinearity III. Fractals 15: Introducing Fractals 16: Dimensions 17: Random Fractals 18: The Box-Counting Dimension 19: When do Averages exist? 20: Power Laws and Long Tails 20: Introducing Julia Sets 21: Infinities, Big and Small IV. Julia Sets and The Mandelbrot Set 22: Introducing Julia Sets 23: Complex Numbers 24: Julia Sets for f(z) = z2 + c 25: The Mandelbrot Set V. Higher-Dimensional Systems 26: Two-Dimensional Discrete Dynamical Systems 27: Cellular Automata 28: Introduction to Differential Equations 29: One-Dimensional Differential Equations 30: Two-Dimensional Differential Equations 31: Chaotic Differential Equations and Strange Attractors VI. Conclusion 32: Conclusion VII. Appendices A: Review of Selected Topics from Algebra B: Histograms and Distributions C: Suggestions for Further Reading
I. Introducing Discrete Dynamical Systems 0: Opening Remarks 1: Functions 2: Iterating Functions 3: Qualitative Dynamics 4: Time Series Plots 5: Graphical Iteration 6: Iterating Linear Functions 7: Population Models 8: Newton, Laplace, and Determinism II. Chaos 9: Chaos and the Logistic Equation 10: The Buttery Effect 11: The Bifurcation Diagram 12: Universality 13: Statistical Stability of Chaos 14: Determinism, Randomness, and Nonlinearity III. Fractals 15: Introducing Fractals 16: Dimensions 17: Random Fractals 18: The Box-Counting Dimension 19: When do Averages exist? 20: Power Laws and Long Tails 20: Introducing Julia Sets 21: Infinities, Big and Small IV. Julia Sets and The Mandelbrot Set 22: Introducing Julia Sets 23: Complex Numbers 24: Julia Sets for f(z) = z2 + c 25: The Mandelbrot Set V. Higher-Dimensional Systems 26: Two-Dimensional Discrete Dynamical Systems 27: Cellular Automata 28: Introduction to Differential Equations 29: One-Dimensional Differential Equations 30: Two-Dimensional Differential Equations 31: Chaotic Differential Equations and Strange Attractors VI. Conclusion 32: Conclusion VII. Appendices A: Review of Selected Topics from Algebra B: Histograms and Distributions C: Suggestions for Further Reading
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