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MAT 241 Analytical Geometry and Calculus III
 Credit Hours:  4 Effective Term: Fall 2015 SUN#: MAT 2241 AGEC: Mathematics Credit Breakdown: 4 Lectures Times for Credit: 1 Grading Option: A/F Only Cross-Listed:

Description: Multivariable calculus including vectors, vector-valued functions, partial differentiation, multiple integration, and an introduction to vector fields.

Prerequisites: MAT 231

Corequisites: None

Recommendations: None

Measurable Student Learning Outcomes
1. (Analysis Level) Examine the use of vectors in plane and in three-dimensional space.
2. (Analysis Level) Describe and compare the motion of an object in the plane or space curve.
3. (Analysis Level) Analyze the graphs of multivariable functions.
4. (Application Level) Solve real- world applications using multivariable derivative.
5. (Evaluation Level) Select multiple integrals to find characteristic attributes of multi-dimensional solids.
6. (Evaluation Level) Intrepret line and surface integrals.
7. (Synthesis Level) Incorporate technology to support problem-solving processes.
Internal/External Standards Accreditation
1a. Accurately perform the operations of vectors.
1b. Find the parametric and symmetric equations of a line in space.
1c. Find an equation of a tangent plane in space.
2a. Correctly use the gradient of a function of two variables in applications.
2b. Find the precise curvatures of graphs represented by various equations.
3a. Thoroughly analyze a multivariable function by examining its contour diagrams (family of level curves) and sketching a three dimensional graph.
3b. Apply the appropriate definitions and rules of continuity, limits to analyze the behavior of multivariable functions
4. Solve optimization and other applied problems using appropriate partial derivatives.
5a. Correctly set up and compute double and triple integrals in rectangular, polar, cylindrical, or spherical coordinates to find the surface area and the volume of a geometric solid.
5b. Use appropriate double or triple integrals to find the mass, center of mass, or moments of inertia of a lamina of variable density.
6a. Use Greens Theorem to correctly evaluate a line integral.
6b. Accurately evaluate surface integrals.
7. Use a graphing calculator or computer software to verify the accuracy of graphs, integrals, and derivatives.