Maricopa Community Colleges  MAT241   19966-20066
Official Course Description: MCCCD Approval: 06/27/95
MAT241 19966-20066 LEC 4 Credit(s) 4 Period(s)
Calculus with Analytic Geometry III
Vector-valued functions of several variables, multiple integration, introduction to vector analysis. Prerequisites: Grade of "C" or better in MAT230 or MAT231.
Go to Competencies    Go to Outline

MCCCD Official Course Competencies:

MAT241   19966-20066 Calculus with Analytic Geometry III
 1. Use plane and space vectors to solve geometry and physics problems. (I) 2. Use space curves to analyze the motion of an object. (II) 3. Use contour diagrams to analyze the behavior of a function of several variables. (III) 4. Use partial derivatives to solve optimization problems. (III) 5. Set up and compute double and triple integrals in any order of integration using rectangular coordinates. (IV) 6. Set up and compute double and triple integrals using polar, cylindrical, and spherical coordinates. (IV) 7. Use line integrals to compute the work done by a vector field along a curve. (V) 8. Use surface integrals to compute the flux of a vector field through a surface. (V) 9. Use multiple integrals to calculate line and surface integrals. (V)
Go to Description    Go to top of Competencies

MCCCD Official Course Outline:

MAT241   19966-20066 Calculus with Analytic Geometry III
I. Space Vectors
A. Definition and comparison with scalars
B. Operations and their properties
2. Scalar multiplication
3. Dot (or scalar) product
4. Cross (or vector) product
C. Representations of lines and planes
D. Applications
II. Vector-Valued Functions
A. Space curves
1. Parametric representation (dynamic view)
2. Representation as the intersection of two surfaces (static view)
3. Arc length
B. Limits
C. Derivatives
D. Integrals
E. Applications
III. Functions of Several Variables
A. Surfaces
1. Representation by contour diagrams (family of level curves)
2. Representation by a graph in three dimensions
B. Limits
C. Derivatives
1. Partial
2. Directional
3. Gradient and its relationship to level curves
4. Tangent plane
D. Optimization problems
1. Second partial derivative test
2. La grange multiplier methods
IV. Multiple Integrals
A. Visualizing the region (plane or solid) of integration
B. Order of integration
C. Change of variables (from Cartesian to)
1. Polar coordinates
2. Cylindrical coordinates
3. Spherical coordinates
D. Applications
V. Vector Fields
A. Line integrals
1. Definition and properties
2. Green's theorem
3. Work done by a vector field over a curve
B. Surface integrals
1. Definition and properties
2. Gauss' divergence theorem
3. Flux of a vector field through a surface
C. Stoke's theorem
Go to Description    Go to top of Competencies    Go to top of Outline