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.
Prerequisite(s)
MATH 1814 with a grade of C or better; or appropriate assessment scores
IAI Number
M1-900B
IAI Title
Calculus for Bsns & Social Sciences
Topical Outline
- Finding domain of functions
- Piecewise-defined functions
- Graphs of functions
- Applications using revenue/cost, equilibrium point, and break-even values
- First and second derivative tests
- Slopes of lines and curves, and their applications including marginal profit/cost/revenue functions
- Limits
- Continuity
- Some rules of derivatives
- Curve sketching
- Optimization and applications including maximizing/minimizing profit, revenue, cost functions
- Additional rules of differentiation including product, quotient, chain, and implicit rules
- Applications using related rates, including changes in production relation to changes in revenue/cost/profit
- Exponential and logarithmic derivatives and their graphs
- Applications of the exponential and natural logarithmic functions, including depreciation/appreciation of assets, investment growth/decay, medicinal dosage decay
- Finite integrals and area under curves, including finding profit/cost/revenue functions from marginals
- Integration by parts, substitution, and the use of tables
- Partial derivatives and their applications, including maxima and minima of functions in more than one variable
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.