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MAT141 - Calculus 1
Catalog Description: Studies functions of a single variable with regard to limits, continuity, differentiation, anti-differentiation, and applications of these topics. Concludes with a study of the definite integral and the fundamental theorem of calculus. Four class hours. Prerequisite: MAT 140 (with a minimum grade of C) or equivalent by placement.
Lecture: 4 hrs.
Course Learning Outcomes (CLOs):
Upon the successful completion of this course, a student will be able to:
1. Compute limits of various functions (polynomial, rational, trigonometric, etc.).
2. Explain the meaning of a limit that exists, or one that fails to exist.
3. Determine whether a function is continuous at a point or on an interval.
4. Compute the derivative of f(x) from the definition of a derivative.
5. Apply appropriate derivative rules (constant, sum, difference, product, quotient, chain, etc.) to find derivatives.
6. Find the equation of the line tangent to the graph of f(x) at a point.
7. Analyze derivatives of a function to describe features on the curve (critical points, inflection points, local extrema, absolute extrema, intervals of increase, intervals of decrease, concavity, etc.)
8. Compute derivatives of implicitly defined functions.
9. Solve related rates problems.
10. Solve optimization problems using differentiation and related techniques.
11. Compute definite and indefinite integrals.
12. Apply u-substitution to integrate functions that can be expressed in the form f(g(x)) g(x).
13. Find the area under the curve of a function using definite integrals.
Effective Term: Fall 2019