An Introduction to Dynamic Systems and Mathematical Modelling

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 intimately bound up with the calculus and considerable knowledge of calculus has been required to use them effectively. The current monograph supposes no knowledge of calculus. Instead, the computer is used to explore the behavior of dynamical systems.