Differential Equations
F05
Norman Derby
Heraclitus taught that the world is in a constant state of flux and the apparent stability of things is just an illusion. Differential equations are the mathematical way of describing change and rates of change. They appear in mathematical models depicting the behavior of any system that can undergo changes: from the solar system, to weather systems, to economic/sociological systems, to chemical and biological systems, to the complicated behavior of nonlinear or chaotic generalized dynamical systems. We will examine mathematical methods for modeling relationships in terms of differential equations and examine specific models in case studies. Learning how to extract useful information from these equations will be the goal of this course. Ordinary differential equations depend upon a single independent variable such as time. You will learn how to solve some ordinary differential equations analytically, how to solve others numerically, and how to squeeze out qualitative information from those that resist solution. Before the term is over, you will be introduced to a few methods for dealing with differential equations involving more than one variable.