Official Course
Description: MCCCD Approval: 3252008 

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. 


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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 vectorvalued
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) 
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Competencies
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. VectorValued 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) 
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