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Nov 24, 2024
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MATH& 148 Business Calculus (5 credits)
Distribution Area Fulfilled Natural Sciences; Quantitative and Symbolic Reasoning; General Transfer Elective
Formerly MATH 157 - CCN
Prerequisite MATH 147 (preferred) or MATH& 141 with a grade of at least 2.0 or instructor permission.
Course Description
Concise course in calculus. Differential and integral calculus of non-trigonometric functions with an emphasis on business and economics applications.
Student Outcomes
LIMITS AND CONTINUITY (content B)
1. Evaluate and interpret limits of functions using numerical, graphical, and algebraic methods with and without a calculator.
2. Determine the continuity of a function graphically and computationally without the calculator.
RATES OF CHANGE AND DIFFERENTIATION (content C, D)
3. Calculate the average rate of change between two points on a function and interpret the answer using the correct units.
4. Estimate the rate of change of a function at a point using the limit of the appropriate average rates of change with and without the calculator.
5. Calculate and interpret instantaneous rates of change and interpret rates of change in applications.
6. Calculate derivatives and values of derivatives of polynomials, rational functions, exponential functions, and logarithmic functions using differentiation techniques including the constant rule, power rule, product rule, quotient rule, and chain rule without the calculator.
7. Calculate derivatives and values of derivatives of higher order without the calculator.
APPLICATIONS OF DIFFERENTIATION (content C, D)
8. Determine where a function is non-differentiable graphically and computationally.
9. Determine the critical value(s), critical point(s), inflection value(s), inflection point(s), interval(s) of increasing, interval(s) of decreasing, concavity, and relative extrema of a function from a graph and computationally with and without the calculator.
10. Given the graph of a function, sketch the graphs of the first and second derivatives.
11. Determine equations of tangent lines and represent and interpret them graphically and in words.
12. Calculate marginal profit, marginal revenue, and marginal cost given a formula, graph or other information for a profit, revenue, and/or cost function.
13. Solve applied optimization problems, such as maximizing profit, minimizing cost, minimizing inventory costs, or maximizing yield.
14. Calculate elasticity of demand and interpret the value
INTEGRATION AND APPLICATIONS (content D, E, F)
15. Determine indefinite integrals of x^n, e^x, ln(x) and any linear combination of these functions.
16. Evaluate proper definite integrals of x^n, e^x, ln(x) and any linear combination of these functions, and use these definite integrals to solve applied problems with and without the calculator.
17. Calculate appropriate indefinite and definite integrals using substitution and a table of integrals.
18. Calculate the area bounded between curves.
19. Approximate the area bounded between curves using left or right endpoint approximation.
20. Interpret the area between curves in applications and use the appropriate units (e.g. interpret the integral of marginal cost as a change in total cost)
21. Use definite integrals to solve applied problems, including finding the consumer’s surplus, producer’s surplus, and average value of a function on an interval.
FUNCTIONS OF SEVERAL VARIABLES (content G)
22. Evaluate a function of several variables.
23. Calculate and evaluate partial derivatives, including first partials, second partials, and mixed partials.
WRITING
24. Use appropriate units when solving application problems. Express solutions to problems correctly in sentences, when appropriate. Use mathematical terms and vocabulary correctly.
GENERAL SKILLS
25. Communicate methods of solution and solutions to problems clearly to their intended audience.
26. Participate actively and responsibly in course activities.
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