Maricopa Community Colleges  MAT241   20086-99999
 Official Course Description: MCCCD Approval: 3-25-2008 MAT241  2008 Fall – 2011 Summer II LEC  4.0 Credit(s)  4.0 Period(s)  4.0 Load  Acad Calculus with Analytic Geometry III Multivariate calculus including vectors, vector- valued functions, partial differentiation, multiple integration and an introduction to vector fields. Prerequisites: Grade of "C" or better in MAT230 or MAT231. Course Notes: Student may receive credit for only one of the following: MAT240 or MAT241.
 MCCCD Official Course Competencies: MAT241  2008 Fall – 2011 Summer II Calculus with Analytic Geometry III

 1. Solve geometry and physics problems using vectors. (I) 2. Analyze the motion of an object using vector-valued functions. (II) 3. Classify and analyze the behavior of functions of several variables. (III) 4. Interpret the geometry of rectangular, polar, cylindrical and spherical coordinate systems. (I, II, III, IV) 5. Solve optimization and other applied problems using partial derivatives. (III) 6. Set up and compute double and triple integrals in any order of integration using rectangular, polar, cylindrical, and spherical coordinates. (IV) 7. Solve physical problems using line integrals and vector fields. (V) 8. Compare alternate solution strategies, including technology. (I, II, III, IV, V) 9. Communicate process and results in written and verbal formats. (I, II, III, IV, V)

 MCCCD Official Course Outline: MAT241  2008 Fall – 2011 Summer II Calculus with Analytic Geometry III

 I. Vectors A. Definitions B. Operations and their properties C. Representations of lines and planes D. Applications II. Vector-Valued Functions A. Definitions and representations B. Limits C. Derivatives D. Integrals E. Applications III. Functions of Several Variables A. Representation of surfaces by 1. Contour diagrams (family of level curves) 2. Graphs in three dimensions 3. Appropriate technology B. Limits and continuity C. Partial derivatives and their applications D. Optimization problems IV. Multiple Integrals A. Visualizing the domain of integration B. Order of integration C. Change of variables 1. Cartesian coordinates 2. Polar coordinates 3. Cylindrical coordinates 4. Spherical coordinates D. Applications V. Vector Fields and Line Integrals A. Definitions B. Properties C. Applications D. Surface integrals (Green's Theorem and Stokes' Theorem) E. Volume integrals (Gauss' Theorem)