Contra Costa College
Course Outline
Department & MATH-290
Number
Course Title Analytic Geometry and Calculus III
Prerequisite MATH-191
Challenge Policy Satisfactory completion of equivalent
course.
Co-requisite
Challenge Policy
Advisory Concurrent enrollment in MATH-875N
*HOURS BY ARRANGEMENT:
0
Number of Weeks
18
Lecture Hours
Lab Hours
*Hours By
Arrangement
Units
90
0
0
5
Hours per term.
ACTIVITIES: (Please provide a list of the activities students will perform in order to
satisfy the HBA requirement):
COURSE/CATALOG DESCRIPTION
This course meets the CSU General Education requirement for Area B4-Mathematics/Quantitative
Reasoning, and the IGETC for Area 2: Mathematical Concepts and Quantitative Reasoning.
This course further develops differential and integral calculus, with emphasis on functions of several
variables, vectors, partial derivatives, multiple integrals, vector integration and vector fields, line and
surface integrals, Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem. Not repeatable.
COURSE OBJECTIVES
At the completion of the course the student will be able to:
1. Perform operations on vectors, including:
(a)
sketch vectors in the plane and in space
(b)
find the dot product and cross product of two vectors
(c)
apply vector products to calculate work and torque
2. Sketch lines, surfaces, and curves in space.
3. Perform operations on vector-valued functions, including:
(a)
differentiation and integration
(b)
determine velocity and acceleration
(c)
compute tangent and normal vectors, arc length, and curvature
4. Perform operations on functions of several variables, including:
(a)
evaluate limits and determine continuity
(b)
compute partial derivatives and differentials
(c)
find directional derivatives and the gradient
(d)
obtain equations of tangent planes and normal lines to a surface in space
(e)
find extrema of functions of two variables
5. Evaluate multiple integrals to find:
(a)
area and volume
(b)
center of mass and moments of inertia
(c)
surface area
6. Use vector fields to:
(a)
evaluate line integrals
(b)
determine path independence
(c)
apply Green's theorem to regions in the plane
(d)
apply Stokes' theorem and the divergence theorem to regions in space
COURSE CONTENT: (In detail; attach additional information as needed and include percentage
breakdown)
20
20
20
20
20
% Vectors and the Geometry of Space
(a)
space coordinates and vectors
(b)
dot product and cross product of vectors
(c)
lines, planes, and surfaces in space
(d)
cylindrical and spherical coordinates
% Vector-Valued Functions
(a)
differentiation and integration
(b)
velocity and acceleration
(c)
tangent and normal vectors
(d)
arc length and curvature
% Functions of Several Variables
(a)
limits and continuity
(b)
partial derivatives and differentials
(c)
directional derivatives and gradients
(d)
tangent planes and normal lines
(e)
extrema of functions of several variables
% Multiple Integration
(a)
iterated integrals
(b)
double integrals and applications
(c)
triple integrals and applications
% Vector Analysis
(a)
vector fields and line integrals
(b)
Green's Theorem
(c)
parametric surfaces and surface integrals
(d)
Divergence Theorem
(e)
Stokes' Theorem
METHODS OF INSTRUCTION
1. Lecture/discussion/demonstration
2. Daily reading assignments from text
3. Homework exercises
INSTRUCTIONAL MATERIALS
Textbook Title:
Author:
Publisher:
Edition/Date:
Calculus : Early Transcendentals
Briggs and Cochran
Addison Wesley
1st edition / 2010
*effective Fall 2014
Textbook Title:
Author:
Publisher:
Edition/Date:
Calculus : Early Transcendentals
Anton, Bivens, and Davis
John Wiley & Sons, Inc.
10th edition / 2012
COURSE EXPECTATIONS (Use applicable expectations)
Outside of Class Weekly Assignments
Weekly Reading Assignments
Weekly Writing Assignments
Weekly Math Problems
Lab or Software Application Assignments
Other Performance Assignments
Hours per
week
5
5 - 10
STUDENT EVALUATION: (Show percentage breakdown for evaluation instruments)
20
80
%
%
%
%
Homework assignments
Exams and quizzes
GRADING POLICY (Choose LG, P/NP, or SC)
X
Letter Grade
90% - 100% = A
80% - 89% = B
70% - 79% = C
60% - 69% = D
Below 60% = F
Pass / No Pass
70% and above = Pass
Below 70% = No Pass
Prepared by: Carol Stanton, Mathematics
Content Review Date: Fall 2013
Revised 04/13
Student Choice
90% - 100% = A
80% - 89% = B
70% - 79% = C
60% - 69% = D
Below 60% = F
or
70% and above =
Pass
Below 70% = No
Pass