Course Description
Introductory calculus will be applied to problems in business and the social sciences. Emphasis will be on applications of basic calculus concepts rather than proofs. Topics include limits; techniques of differentiation applied to polynomial, rational, exponential, and logarithmic functions; partial derivatives and applications; finding the minima and maxima of functions; and integration techniques such as substitution and integration by parts. IAI: M1 900-B
Prerequisite(s)
MATH 1814 College Algebra with a grade of C or better; or appropriate assessment scores - Must be completed prior to taking this course.
At the end of this course, students will be able to:
- Find limits numerically, graphically, and algebraically.
- Apply the patterns of differentiation to find the derivative of a given function.
- Solve basic differentiation problems including higher-order derivatives and finding extrema within business and social science contexts.
- Compute integrals using various methods including substitution, parts, and tables.
- Solve integration problems, including finding area and approximate integration.
- Apply the concepts of limits, derivatives and integrals to solve problems involving functions unique to business and social science applications and interpret the results.
Topical Outline
1. Finding domain of functions
2. Piecewise-defined functions
3. Graphs of functions
4. Applications using revenue/cost, equilibrium point, and break-even values
5. First and second derivative tests
6. Slopes of lines and curves, and their applications including marginal profit/cost/revenue functions
7. Limits
8. Continuity
9. Some rules of derivatives
10. Curve sketching
10. Curve sketching
11. Optimization and applications including maximizing/minimizing profit, revenue, cost functions
12. Additional rules of differentiation including product, quotient, chain, and implicit rules
13. Applications using related rates, including changes in production relation to changes in revenue/cost/profit
12. Additional rules of differentiation including product, quotient, chain, and implicit rules
13. Applications using related rates, including changes in production relation to changes in revenue/cost/profit
14. Exponential and logarithmic derivatives and their graphs
15. Applications of the exponential and natural logarithmic functions, including depreciation/appreciation of assets, investment growth/decay, medicinal dosage decay
16. Finite integrals and area under curves, including finding profit/cost/revenue functions from marginals
17. Integration by parts, substitution, and the use of tables
18. Partial derivatives and their applications, including maxima and minima of functions in more than one variable