MAT142

Calculus 2

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 ‘C’ or higher or by placement.

Course Learning Outcomes:

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: Fall 2023

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