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# University Catalog

### MATH 221. Calculus I

Credits: 4
 Department: Mathematics & Statistics Description: Limits, continuity, differentiation, applications of derivatives, integration. Prereq.: 115, or 112 and 113, or high school advanced algebra and trigonometry with a satisfactory math placement score. 4 Cr. F, S, SUM. Prerequisites: MATH 115, or MATH 112 and MATH 113, or high school advanced algebra and trigonometry with a satisfactory math placement score. Semester Offered: FallSpringSummer Grading Method: ABCDF Lab: Lab Goal Area: GOAL AREA 4: MATHEMATICAL THINKING & QUANTITATIVE REASONING Additional Information:

#### Student Learning Outcomes

 1 Calculate limits using graphical, algebraic and numerical methods and the Squeeze Theorem. 2 Determine continuity of a function at points, identify various types of discontinuities and identify intervals of continuity for functions. 3 Calculate derivatives from the definition and using differentiation rules and implicit differentiation. 4 Use differentiation to identify tangent lines, to solve geometric problems and to solve problems involving rates of change. 5 Solve optimization and related-rates problems by analytic methods. 6 Graph a function, showing all relevant information such as relative extrema, inflection points, and asymptotes, with analytic methods and without the aid of graphing technology. 7 Approximate roots of equations by using the bisection method and Newton’s method. 8 Calculate integrals by using the Fundamental Theorem of Calculus, u-substitution, and observations about symmetry of graphs. Use integration to find the area under a curve, to solve problems involving net change, and to solve other geometric problems. 9 State and apply named theorems of calculus (the Intermediate Value Theorem, the Mean Value Theorem, and the Fundamental Theorem of Calculus). Identify whether a derivative or an integral (or neither) is more appropriate for use in a given problem. 10 Communicate their knowledge of the basic principles of Calculus I, both orally (e.g. class discussions) and in writing (e.g. written assessments).

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