# Genesee Course Listing

## Official Course Information

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Summer 2022

### Mathematics Courses:

or

#### MAT142 - Calculus 2

Credits: 4

Catalog Description: Examines applications of the definite integral; analysis of the natural logarithmic, exponential, trigonometric, and hyperbolic functions; introduction to differential equations; techniques of integration; L'Hopital's Rule and indeterminate forms; improper integrals; and infinite series. Prerequisite: MAT 141 with a grade of āCā or higher or by placement.

Lecture: 4 hrs.

Course Learning Outcomes (CLOs):
Upon the successful completion of this course, a student will be able to:
1. Evaluate the derivative of any transcendental function (exponential, logarithmic, trigonometric, or inverse trigonometric).
2. Integrate using various techniques of integration (fundamental integral formulas, u-substitution, integration by parts, powers of trigonometric functions, trigonometric substitution, partial fractions, integral tables).
3. Apply the Fundamental Theorem of Calculus to evaluate a definite integral.
4. Find the area between two curves, using integrals.
5. Sketch any plane region defined by one or more simple curves, finding the volume of the solid generated by revolving the plane region about the x- or y-axis, using integrals.
6. Apply any of the standard approximation techniques (midpoint, trapezoid, Simpson's) to evaluate a definite integral involving any simple function (accurate to three decimal places).
7. Use L'Hopital's Rule to evaluate any limit involving the indeterminate form 0/0 or oo/oo.
8. Determine the convergence or divergence of an infinite series using various convergence/divergence tests (divergence, ratio, root, comparison, direct comparison, limit comparison, geometric, harmonic, integral, p-series).
9. Find the interval of convergence given a power series.
10. Find a Taylor polynomial or Taylor series at a given point for a function of a single variable.

Effective Term: Spring 2020