### MATH 2633

This is an archive of the Common Course Outlines prior to fall 2011. The current Common Course Outlines can be found at http://www.gpc.edu/programs/Common-Course-Outlines.
Credit Hours   4
Course Title   Calculus III
Prerequisite(s)   MATH 2432 with a "C" or better
Corequisite(s)   None Specified
Catalog Description
This course includes the study of vectors, solid analytical geometry, partial derivatives, multiple integrals, line integrals, and applications.

Expected Educational Results
As a result of completing this course, the student will be able to:
1. Find equations of lines and planes in three dimensions.
2. Find arc length, curvature, and the moving trihedral for vector functions and space curves.
3. Calculate and apply partial derivatives.
4. Calculate and apply double and triple integrals.
5. Calculate line integrals.

General Education Outcomes
As a result of completing this course, the student will be able to:
1. Find equations of lines and planes in three dimensions.
2. Find arc length, curvature, and the moving trihedral for vector functions and space curves.
3. Calculate and apply partial derivatives.
4. Calculate and apply double and triple integrals.
5. Calculate line integrals.

Course Content
1. Vectors
2. Partial Derivatives
3. Multiple Integrals
4. Line Integrals
ENTRY LEVEL COMPETENCIES
Upon entering this course the student should be able to do the following:
1. Investigate limits using algebraic, graphical, and numerical techniques.
2. Investigate derivatives using the definition, differentiation techniques, and graphs.
3. Apply the derivative as a rate of change, optimize functions, use Newton's Method, and sketch curves.
4. Define the definite integral and approximate definite integrals using Riemann sums.
5. State and apply the Fundamental Theorem of Calculus.
6. Graph and use parametric equations.
7. Evaluate integrals using techniques of integration.
8. Use integrals to solve application problems.
9. Solve separable differential equations and apply to elementary applications.
10. Differentiate and integrate algebraic, trigonometric, exponential, logarithmic, and inverse trigonometric functions. Differentiate implicit functions.
11. Investigate the convergence of series and apply series to approximate functions and definite integrals.
12. Apply polar representations including graphs, derivatives, and areas.

Assessment of Outcome Objectives