MAT 146 - Applied Business Calculus
Review of analytic geometry of lines and parabolas; functions, and their graphs; limits and continuity; differentiation rules and applications; integration techniques and applications; exponential and logarithmic functions and applications. Recommended for Social Science, Health Science and Business students. Not for Mathematics majors or Science majors in the A.S. Degree program.
Prerequisite: MAT 136 Intermediate Algebra and Trigonometry or equivalent
3 Class Hours
Learning Outcomes of the Course:
Upon successful completion of this course the student will be able to:
1. After a brief review:
- Write and recognize the equations of lines and parabolas.
- Define a function and determine the domain of a given function.
- Graph polynomials, rational functions and functions involving radicals.
- Find the points of intersection of two functions.
- Understand the composition of functions.
2. Understand the concept of limit and use limit rules to evaluate limits.
3. Understand the concept of continuity and find points of discontinuity of a given function.
4. Evaluate limits from a given graph.
5. Define a derivative and find derivatives of functions using the definition.
6. Understand the geometric interpretation of a derivative (slope of tangent line).
7. Understand the difference between a function and its derivative on a graph.
8. Use the rules of differentiation to find derivatives of more complex functions.
9. Find a relative extrema and inflection points of a function.
10. Use differentiation to solve max-min problems and to aid in curve sketching.
11. Find anti-derivatives of functions.
12. Evaluate definite integrals using the Fundamental Theorem of Calculus.
13. Understand the geometric interpretation of the definite integral (area under curve).
14. Graph logarithmic and exponential functions.
15. Apply the properties of logarithms and exponents to solving equations (e.g., growth, compound interest, present value).
16. Differentiate and integrate logarithmic and exponential functions and apply this knowledge to solve problems in business and economics.
17. Apply differentiation (rate of change of a function) to solve problems in business and economics (e.g., marginal cost and revenue, maximization of profits).
18. Apply integration to solve problems in business and economics (e.g., total value, expected value).
This course prepares students to meet the Mathematics General Education requirement.
In the context of the course objectives listed above, upon successful completion of this course the student will be able to:
1. Interpret and draw inferences from mathematical models such as formulas, graphs, tables and schematics.
2. Represent mathematical information symbolically, visually, numerically and verbally.
3. Employ quantitative methods such as arithmetic, algebra, geometry, or statistics to solve problems.
4. Estimate and check mathematical results for reasonableness.
5. Recognize the limitations of mathematical and statistical methods.
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