MAT 220 - Business Calculus

 
Description
This calculus course is tailored for business and social science majors. Students develop skills in fundamental differentiation and integration techniques applied to real-world contexts. Students explicitly and implicitly differentiate polynomial, rational, exponential and logarithmic functions. Graphing techniques leverage an understanding of how a function’s first and second derivatives relate to maximization, minimization and curve shape. Definite and indefinite integration techniques are practiced. Multivariate optimization through partial differentiation of functions of multiple variables is also covered. Upon completion, students are equipped with analytical tools vital for quantitative analysis in business, economics and related fields.

1. Compute limits of polynomial, rational, exponential and logarithmic functions.
2. Identify intervals in which polynomial, rational, exponential and logarithmic function are continuous.
3. Apply differentiation techniques to polynomial, rational, exponential and logarithmic functions, including those that require implicit differentiation.
4. Apply differentiation techniques to find the following for a given function: intervals where increasing, intervals where decreasing, extrema, inflection points and concavity.
5. Construct the graph of a function based on its first and second derivative.
6. Solve optimization problems using the derivative.
7. Evaluate the indefinite integral of a function.
8. Calculate the definite integral of a function.
9. Compute the area of a region using the definite integral.
10. Solve application problems using the definite integral.
11. Apply differentiation techniques to multivariate functions.
12. Utilize partial derivatives in optimization problems involving multivariate functions, including those subject to constraining conditions.

 Listed Topics

1. Functions, limits and continuity
2. Differentiation: The derivative of a function, techniques of differentiation, higher order derivatives and the chain rule, including differentiation of exponential and logarithmic functions and implicit differentiation
3. Applications of the derivative: graphing and finding maxima and minima of functions
4. Applications of differentiation
5. Integration: antiderivatives, indefinite integral, techniques of integration, definite integral, area under and between curves
6. Applications of integral calculus in business and the social sciences
7. Multivariate calculus: partial derivatives, maximal and minima, maxima and minima subject to constraining conditions using LaGrange multipliers
8. Applications of multivariate calculus

• Critical Thinking & Problem Solving
• Quantitative & Scientific Reasoning

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