MAT 165 - Business Calculus

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 1: Define exponential functions.
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.