A First Course in Discrete Dynamical Systems

By Richard A. Holmgren

Discrete dynamical systems are essentially iterated functions. Given the ease with which computers can do iteration, it is now possible for anyone with access to a personal computer to generate beautiful images whose roots lie in discrete dynamical systems. Images of Mandelbrot and Julia sets abound in publications both mathematical and not. The mathematics behind the pictures are beautiful in their own right and are the subject of this text. The level of the presentation is suitable for advanced undergraduates with a year of calculus behind them. Students in the author's courses using this material have come from numerous disciplines; many have been majors in other disciplines who are taking mathematics courses out of general interest. Concepts from calculus are reviewed as necessary. Mathematica programs that illustrate the dynamics and that will aid the student in doing the exercises are included in an appendix.

• Format: Paperback
• Language: English
• ISBN: B00E86KV9W
• ISBN13: 9780387947808
• Release Date: August 1996
• Publisher: Springer
• Length: 223 Pages
• Weight: 0.80 lbs.
• Dimensions: 0.6" x 6.1" x 9.2"

Customer Reviews

Amazing motivational introduction

An excellent short motivational reading / introductory course material. Starts ground up and uses very simple hands-on examples to demonstrate the fascinating behavior of non-linear dynamic systems (chaos, fractals, etc). Covers most of the basic methodology. The book also has a lot of excellent exercises for reinforcing the material, for different difficulty levels.

An excellent book

This is an excellent book for teaching for mathematics students. Besides the standard material it contains a chapter about some numerical methods as dynamical systems. I strongly propose that a third updated edition is made.