MAC 2313--CALCULUS WITH ANALYTIC GEOMETRY III
Catalog Description:
(4) (A.A.) Four hours lecture per week. Prerequisite: MAC 2312. 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 2312, with
vectors in 2 and 3 space, and differentiation and integration of functions of several
variables.
Performance Standards:
Upon completion of this course the student will be able to do the following with a
mastery level of 70%.
1. Calculate the cross product of two vectors.
2. Write and interpret parametric equations for a line in 3-space.
3. Write and interpret an equation for a plane in 3-space.
4. Sketch simple 3-space surfaces.
5. Recognize and analyze equations for quadric surfaces. Sketch.
6. Use cylindrical and spherical coordinates to write equations.
7. Differentiate and integrate vector valued functions.
8. Analyze space curves using tangential, normal and binomial vectors.
9. Find limits and check continuity for functions of several variables.
10. Calculate partial derivatives and gradient vectors.
11. Find directional derivatives and gradient vectors.
12. Find and equation for the plane tangent to a surface at a point.
13. Find parametric equations for the line normal to a surface at a point.
14. Use differentials to find a linear approximation to a function and estimate the
error involved.
15. Find maxima, minima, and saddle points for surfaces in 3-space.
16. Use LaGrange multipliers to find maxima and minima for a function under
restraint conditions.
17. Calculate and interpret double integrals in rectangular coordinates in polar
coordinates.
18. Calculate and interpret triple integrals in rectangular, cylindrical, and spherical
coordinates.
Date of Last Revision: April 1, 2002