MCCCD Program Description

Calculus with Analytic Geometry III

Course: MAT241

First Term: 2011 Fall

Lecture 4 Credit(s) 4 Period(s) 4 Load
Subject Type: Academic
Load Formula: S

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

MCCCD Official Course Competencies
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 Competencies must be coordinated with the content outline so that each major point in the outline serves one or more competencies. MCCCD faculty retains authority in determining the pedagogical approach, methodology, content sequencing, and assessment metrics for student work. Please see individual course syllabi for additional information, including specific course requirements.

MCCCD Official Course Outline
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)

MCCCD Governing Board Approval Date: 3/25/2008

All information published is subject to change without notice. Every effort has been made to ensure the accuracy of information presented, but based on the dynamic nature of the curricular process, course and program information is subject to change in order to reflect the most current information available.