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# MAT 165 - Business Calculus

Course Department: Mathematics
Last Date of Approval: Fall 2017

3 Credits
Total Lecture Hours: 45
Total Lab Hours: 0
Total Clinical Hours: 0
Total Work-Based Experience Hours: 0

Course Description:
This course is a study of the concepts and skills of calculus which have important applications in business, economics, psychology, social science, and natural science. Topics included are functions, limits, differentiation and its applications, and integration and its applications. This course will also help students gain mathematical literacy which will be of vital significance when making important life decisions. In addition, this course will help with any career that involves mathematics, decision making, or problem-solving.

Prerequisites: MAT 102 - Intermediate Algebra  with C grade or better or the necessary score on the mandatory assessment and placement chart found in the course catalog.
Mode(s) of Instruction: face-to-face

Credit for Prior Learning: There are no Credit for Prior Learning opportunities for this course.

Course Fees: None

Common Course Assessment(s): None

Student Learning Outcomes and Objectives:
Outcome 1: Recognize and analyze the various classes of functions.
Task 1: Determine the characteristics, the properties and the graphs of various functions.
Task 2: Identify some important functions such as linear functions, power functions, absolute value functions and their properties and other attributes.
Task 3: Determine the zeros of various functions by algebraic and graphing processes.
Task 4: Construct appropriate functions and equations and their graphs to solve many and varied applied problems in the real world of business, science, economics and other areas.

Outcome 2: Demonstrate an understanding of, and apply the definition of, the derivative concept.
Task 1: Define and develop an understanding of the concept of the slope of a line.
Task 2: Use the concept of the slope in determining the equation of the tangent line at a point on a curve.
Task 3: Define and develop the notion of a limit and indicate how it relates to the concept of the derivative.
Task 4: Develop the relationship between differentiability and continuity of a function at a given point.
Task 5: Give full definition to the derivative.
Task 6: Use the constant-multiple rule, the sum rule and the general power rule of differentiation to extend the number and types offunctions that can be differentiated.
Task 7: Look at other notations for derivatives such as y’, dy/dx, df/dx, and f’(x).
Task 8: Determine the second derivative of various functions.
Task 9: Use the derivative as a method to indicate the rate of change concept.

Outcome 3: Use the derivative in determining solutions to applied problems in a variety of real life situations.
Task 1:    Describe the graphs of functions and what their features mean to the function.
Sub-Task 1: Defining an increasing function interval.
Sub-Task 2: Defining a decreasing function interval.
Sub-Task 3: Defining extreme points (maximums and/or minimums).
Sub-Task 4: Defining increasing and/or decreasing slopes on an interval.
Sub-Task 5: Determine intercepts, undefined points and asymptotes.
Task 2: Develop an understanding of the first and second derivative rules.
Task 3: Use the various rules for derivatives of functions and the various   properties such as extremes and inflection points and intercepts to develop techniques for curve sketching.
Task 4:    Apply the concepts of the derivative(s) to determine the solution to “optimization” problems.
Task 5: Solve business, industrial, economic, geometric, etc. types of application problems that involve the “optimization” concept.
Task 6: Apply the features of Calculus to solving business and economics  problems.

Outcome 4: Develop and apply various additional techniques of differentiation-Product Rule, Quotient Rule, Chain Rule.
Task 1: Use the product and quotient rules to differentiate functions.
Task 2: Use the discussion and definition of the limit concept to differentiation to verify the Product and Quotient rules.
Task 3: Develop the general power rule and the Chain rule to differentiate functions.

Outcome 5: Define exponential and logarithmic functions, identify their properties and applications, and utilize their differentiation techniques.
Task 2: Understand the extensive use of the exponential function.
Task 3: Develop the rules for differentiating exponential functions.
Task 4: Define logarithmic functions and understand their properties.
Task 5: Define the natural logarithmic function ln(x) and understand its extensive application.
Task 6: Illustrate the relationships between logarithmic and exponential functions.
Task 7: Find the derivative of logarithmic functions.
Task 8: Apply the properties and the differentiation processes of logarithmic and exponential functions to problems in everyday life.

Outcome 6:Demonstrate an understanding of the integral concept and of calculation techniques for the definite integral.
Task 1: Define anti-differentiation and use it to approximate area under a curve.
Task 2: Define the Fundamental Theorem.
Task 3: Find areas in the xy plane.
Task 4: Solve application problems of the Definite Integral.
Task 5: Solve Integration problems by substitution.

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