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A First Course In Discrete Dynamical Systems (Universitext)-used
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1.1. Phase Portraits. Exercise Set 1. A Quick Look At Functions. Exercise Set 2. The Topology Of The Real Numbers. Exercise Set 3. Periodic Points And Stable Sets. 4.1 Graphical Analysis. Exercise Set 4. Sarkovskiis Theorem. Exercise Set 5. Differentiability And Its Implications. Exercise Set 6. Parametrized Families Of Functions And Bifurcations. Exercise Set 7. The Logistic Function Part Cantor Sets And Chaos. 8.1. A First Look At The Logistic Function When R ≫ 4. 8.2. Cantor Sets. 8.3. Chaos And The Dynamics Of The Logistic Function. 8.4. A Few Additional Comments On Cantor Sets. Exercise Set 8. The Logistic Function Part Topological Conjugacy. Exercise Set 9. The Logistic Function Part A Perioddoubling Cascade. Exercise Set 10. The Logistic Function Part Symbolic Dynamics. 11.1. Symbolic Dynamics And Metric Spaces. 11.2. Symbolic Dynamics And The Logistic Function. Exercise Set 11. Newtons Method. 12.1 Newtons Method For Quadratic Functions. 12.2 Newtons Method For Cubic Functions. 12.3 Intervals And Rates Of Convergence. Exercise Set 12. Numerical Solutions Of Differential Equations. Exercise Set 13. The Dynamics Of Complex Functions. 14.1. The Complex Numbers. 14.2. Complex Functions. 14.3. The Dynamics Of Complex Functions. 14.4. The Riemann Sphere. 14.5. Newtons Method In The Complex Plane. Exercise Set 14. The Quadratic Family And The Mandelbrot Set. 15.1 Generating Julia And Mandelbrot Sets On A Computer. Exercise Set 15. A.L. Iterating Functions. Finding The Value Of A Point Under Iteration. Tables Of Iterates. Controlling The Precision Of The Computations. Graphing Iterated Functions. A.2. Graphical Analysis. A.3. Bifurcation Diagrams. A.4. Julia Sets. A.5 The Mandelbrot Set. A.6 Stable Sets Of Newtons Method. References. Dynamical Systems. General Interest Books On Dynamics. Topics In Mathematics. Computer Programs And Algorithms.
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- Q: What are the dimensions of this book? A: The dimensions of this book are six point one inches by nine point two five inches.
- Q: How many pages does the book have? A: This book contains two hundred twenty-six pages.
- Q: What type of binding does this book have? A: The book is paperback bound.
- Q: Who is the author of this book? A: The author of this book is Richard A. Holmgren.
- Q: What topics are covered in this book? A: The book covers topics such as phase portraits, periodic points, and the dynamics of complex functions.
- Q: What is the reading level of this book? A: This book is suitable for advanced undergraduate or graduate students studying mathematics.
- Q: How do I approach the exercises in this book? A: You can approach the exercises by first reviewing the associated theory and concepts presented in the chapters.
- Q: Is this book suitable for self-study? A: Yes, this book is suitable for self-study as it includes exercises and references to enhance understanding.
- Q: What prerequisites are needed to understand this book? A: A background in basic calculus and linear algebra is recommended to fully grasp the concepts.
- Q: How should I store this book? A: Store the book in a cool, dry place, upright or flat to prevent damage to the pages or cover.
- Q: Can I use this book for a course in differential equations? A: Yes, this book is suitable for courses focusing on differential equations and dynamical systems.
- Q: What if my book arrives damaged? A: If your book arrives damaged, you should contact the seller to discuss return or replacement options.
- Q: Is there a warranty for this book? A: Typically, books do not come with a warranty, but check with the seller for their return policy.
- Q: What topics are emphasized in the exercises? A: The exercises emphasize topics such as graphical analysis, symbolic dynamics, and numerical solutions.
- Q: What is the purpose of the references section in this book? A: The references section provides additional resources for further reading and research on dynamical systems.
- Q: Is this book beginner-friendly? A: No, this book is not beginner-friendly and is intended for those with prior knowledge of mathematics.