Biology, Psychology
& Medicine
  Calculus
& Differential Eqs.
  Physical Science
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 This volume is part of the monograph series of the New Liberal Arts Program (1980-1992), a project of the Alfred P. Sloan Foundation. The NLA Program had the goal of assisting in the introduction of quantitative reasoning and concepts of modern technology within liberal education. The Program was based on the conviction that college graduates should have been introduced to both areas if they are to live in the social mainstream and participate in the resolution of policy issues. The Center for Mathematics and Quantitative Education is delighted to make these monographs available.

 

AN INTRODUCTION TO DYNAMIC SYSTEMS AND MATHEMATICAL MODELLING


Donal O'Shca
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 dynamical systems.

Chapler Coverage

  • 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.