AN INTRODUCTION TO DYNAMIC SYSTEMS
AND MATHEMATICAL MODELLING
Mount Holyoke Collcge
The primary aim of this monograph is to expose some models which
have been central in the development of mathematical modelling and which
exemplify the process of using mathematics to understand the world. The author
shows how mathematics can be, and is, used as a speculative tool. Computer
exploration makes this exploratory side of mathematics accessible to students
with a solid high school background.
The monograph focuses primarily on dynamical systems, which three
centuries of experience have shown to be the most useful class of mathematical
models. Historically, the discovery and use of dynamical systems have been
inlimately bound up with the calculus and considerable knowledge of calculus
has been required to use them effectively. Thc current monograph supposes no
knowledge of calculus. Instead, the computer is used to explore the behavior of
- Model of snakes on Guam
- Ecological models including species in symbiosis and predatorprey models
- Dynamical systems including state space, equilibrium points, and limit cycles
- Greatest mathematical model—Kepler, Galileo, and Newton
- Dynamical systems and determinism including structural stability and chaotic systems
This is written from the mathematical viewpoint. The main applications
are in ecology and planetary motion and these are extensively developed.
There is also a little bit about the Lorenz Attractor. Exercises are
interspersed throughout the volume.