Calculus Functions and their Applications

The course is mainly focused on the applications of functions in real life problems. The course concentrates on various types of functions such as linear, quadratic, polynomial, exponential, logarithmic, logistic, and rational.

In the beginning of each section, we go through a brief overview of the mathematical aspect of each type of function and then we present their applications through word problems.

After introducing functions and their applications, we move to the derivative. We begin with an overview on limits and then proceed to the definition of the derivative as the limit. We see the geometric interpretation of it as the slope of the tangent line and as the instantaneous rate of change.  We then proceed to various differentiation  techniques and to the first and second derivative tests. The maximum and minimum points of functions are found using the derivative tests constructing the appropriate sign tables. The concavity of functions is discussed. Then, we examine applications of maximum and minimum points such as maximizing the profit function or minimizing the cost function.