MAC 2312 - CALCULUS WITH ANALYTIC GEOMETRY II
Catalog Description:
(4) (A.A.) Four hours lecture per week. Prerequisite: MAC 2311. This course meets
Area II requirements for both the A.A. general education requirements and the A.S.
general education requirements. This course is a continuation of MAC 2311, with
differentiation and integration of logarithmic, exponential and trigonometric functions,
polar coordinates, improper integrals and infinite sequences and series.
Performance Standards:
Upon completion of this course the student will be able to do the following with a
mastery level of 70%.
1. Find volumes of revolution using the Disc and Shell Methods.
2. Determine arc length and Surface areas of revolution.
3. Solve applications of integration problems involving work, moments and centers
of mass, and pressure and force.
4. Evaluate integrals analytically, using substitution, integration by parts, using
trigonometric substitution and identities, and partial fractions.
5. Apply L’Hôpital’s to evaluate limits of indeterminate forms.
6. Evaluate convergent improper integrals.
7. Use the comparison, ratio, alternating series, and integral tests to test convergence
of an infinite series, and understand the role of the sequence of partial sums in
determining convergence.
8. Test for conditional and absolute convergence, and estimate the sum, of an
alternating series.
9. Find Maclaurin and Taylor polynomials and bound the error in using such a
polynomial to approximate a function.
10. Find a power series representation for a function, and determine where it
converges.
11. Define conic sections in both polar and parametric form.
12. Find the slope and tangent lines, arc length, and area if a surface of revolution of
parametric and polar equations.
Date of Last Revision: April 1, 2002