# Calculus for the Social and Managerial Sciences

MTH 160

## Course Description

Prerequisite: MATH LEVEL 8, or MTH 120 or MTH 121 or MTH 122 or MTH 151 with a "C" or better or three and a half years of high/school-college preparatory mathematics. Satisfies the mathematics requirements for students majoring in business or social sciences. Covers topics including graphing, differentiation, and integration of functions (algebraic, exponential, and logarithmic), and the use of these techniques within business and economic models. A GRAPHING CALCULATOR IS REQUIRED. (60-0)

## Outcomes and Objectives

### Demonstrate an understanding of the mathematical concepts of limit and continuity.

#### Objectives:

• Determine the existence of a limit algebraically or from a graph of the function.
• Determine one-sided and two-sided limits algebraically or from a graph of the function.
• Determine the continuity of a function at a point from the definition of continuity at a point or from the graph of the function.

### Demonstrate an understanding of the mathematical concept of derivative.

#### Objectives:

• State the definition of a derivative.
• Use the different interpretations of a derivative appropriately.
• Approximate the value of a derivative of a function at a point from a graph of the function.
• Use the formulas to determine the derivatives (first derivative, second derivative, partial derivative) of polynomial, rational, exponential, logarithmic and radical functions.
• Determine, from the graph of the function, each point where the derivative of the function does not exist.

### Demonstrate an understanding of the mathematical concept of integration.

#### Objectives:

• Evaluate indefinite integrals of elementary polynomial, rational, and exponential function.
• Define the definite integral using the concept of a limit.
• Appropriately use tables of integrals to determine the integral of a function.
• Determine the numerical value of a definite integral.

### Demonstrate an understanding of the relationship between the concepts of limit, continuity, derivation, and integration.

#### Objectives:

• State the relationship between differentiation and integration.
• State the relationship between the existence of a limit, the continuity of a function, and the existence of a derivative of a function at a point.

### Demonstrate an understanding of how derivatives and integrals can be used to solve problems.

#### Objectives:

• Determine the nature of a function (increasing or decreasing, concavity, inflection points, maximums or minimum) using derivatives.
• Use the derivative as a measure of rate of change in applied problems.
• Use integration to determine the total amount of change in a function in applied problems.
• Use an integral to determine area.
• Use numerical integration techniques to approximate definite integrals.

### Communicate effectively about calculus.

#### Objectives:

• Use the specialized notation of derivatives and integrals appropriately.
• Describe solutions to problems, both verbally and in written form, using appropriate terminology.