Introduction

Mathematical modeling is an attempt to describe how the real world works using mathematics and symbols. Models can help us understand and predict the behavior of a system, or investigate the impacts of various components on its behavior. Consequently, mathematical modeling is increasingly used in the natural sciences (physics, chemistry, biology, etc.), engineering, the social sciences (sociology, economics, psychology, etc.), and even music and linguistics.

In many situations mathematical models involve the search for an unknown function whose derivatives satisfy an equation. Such equations are called differential equationss. We obviously want to find a solution of a given differential equation. However, you’ll discover as the course progresses that studying differential equations entails more than merely knowing techniques developed by others to solve them.

Since learning the terminology of any specialized subject is essential for studying that subject, we start with definitions, and some basic concepts of differential equations.