MTH 210 - Calculus I
A first course in single variable calculus. Topics include limits and continuity; differentiation of algebraic, trigonometric, exponential, logarithmic, and inverse trigonometric functions; applications of derivatives to curve sketching, related rates, optimization, and rectilinear motion; indefinite and definite integrals; both parts of the Fundamental Theorem of Calculus; applications of definite integrals to area, average value, and rectilinear motion; and integration by u-substitution. A specific calculator may be required of students in this course. Students are advised to check with the instructor.
Prerequisite: MTH 175 with grade of C or higher, or high school precalculus course taken within the last three years with a grade of B (83) or higher, or MCC Level 10 Mathematics placement.
New SUNY General Education: SUNY - Mathematics (and Quantitative Reasoning)
Retiring SUNY General Education: SUNY-M - Mathematics (SMAT)
MCC General Education: MCC-CT - Critical Thinking (MCT), MCC-QL - Quantitative Literacy (MQL)
Course Learning Outcomes
1. Determine a variety of limits which may include any of the following types: one-sided limits, two-sided limits, infinite limits, or limits at infinity.
2. Determine whether a function is continuous at a given point.
3. Differentiate a variety of functions using the limit definition of the derivative.
4. Determine whether a function is differentiable at a given point.
5. Differentiate combinations or compositions of a variety of functions which may include any of the following: polynomial, radical, rational, trigonometric, inverse trigonometric, exponential, or logarithmic.
6. Differentiate implicitly defined functions.
7. Use derivatives to determine key features of graphs of functions which may include any of the following: intervals of increase or decrease, intervals of concavity, extrema, or points of inflection.
8. Determine indefinite integrals.
9. Approximate definite integrals with Riemann Sums.
10. Apply the Fundamental Theorem of Calculus.
11. Use the method of integration by u-substitution.
12. Use methods of Calculus to solve a variety of applications which may include any of the following types: related rates, optimization, rectilinear motion, area, or average value.
Course Offered Fall, Spring