Although financial models are theoretical frameworks, we often use mathematical tools to work with these models. Mathematical models usually consist of a set of equations, which are designed to describe the structure of the model, and whose solution determines the importance of variables. This week, we will look at equations, including the basic terminology, and the rules for solving equations requiring more than one operation.

Functions are important in every area of pure and applied mathematics, including mathematics applied to economics, finance and business. For example, the language of economic analysis is full of terms like demand and supply functions, cost functions, production functions, consumption functions, and so on. This week, we will present a discussion of functions of one real variable, illustrated by some economic examples. Remember- one variable is a function of another if the first variable depends upon the second.

An important topic in many scientific disciplines- including economics- is the study of how quickly quantities change. The concept used to describe the rate of change of a function is known as the derivative. In this lecture, we will define the derivative of a function, and share some of the important rules for calculating it.