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6.
Hours per week of independent work done outside of class: 8
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Course Preparation –
(Supplemental form B required)
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7a. Prerequisite(s): (Course and/or other
preparation/experience that is REQUIRED to be completed
previous to enrollment in this course.)
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Completion of Math. 31 or equivalent with
a grade of "C" or better
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7b. Co-requisite(s): (Courses and/or
other preparation that is REQUIRED to be taken concurrently with
this course.)
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7c. Advisory: (Minimum preparation RECOMMENDED in
order to be successful in this course. Also known as “Course Advisory”.)
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Catalog Description And Other Catalog Information
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8. Repeatability:
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Not Repeatable
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9a. Grading Option:
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Standard Grade
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9b. Catalog Description:
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Continuation of Math. 31. Vectors and
analytic geometry in the plane and space; functions of several
variables; partial differentiation, multiple integrals, and
application problems; vector functions and their derivatives;
motion in space; and surface and line integrals, Stokes'' and
Green''s Theorems, and the Divergence Theorem. (CAN MATH 22)
(with Math 30 & 31, CAN MATH SEQ C)
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Course Outline Information
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10. Student Performance Outcomes: (Outcomes for all
credit courses must indicate that students will learn critical
thinking and will be able to apply concepts at college
level. Outcomes must be related to items listed in
Section 11.)
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1. compute vector quantities such as the
dot product and the
magnitude of a vector;
2. write the equation of a line or a plane in space using vector
methods;
3. solve problems dealing with the motion of a particle in the
plan
or in space using vectors methods;
4. calculate the length of a curve in 3-space;
5. graph and identify quadric surfaces;
6. sketch functions of two variables, level curves of functions
of
two variables, and level surfaces of functions of three
variables;
7. find maximum and minimum values of functions of two variables
and
solve applied max/min problems;
8. compute partial derivatives of functions of more than one
variable;
9. solve maximum and minimum problems using Lagrange multipliers;
10. evaluate double and triple integrals using rectangular,
polar,
cylindrical, or spherical coordinates;
11. compute area, volume, centers of mass, and moments of inertia
using double and triple integration;
12. evaluate line integrals and solve related applied problems;
13. evaluate line integrals and areas using Green''s Theorem;
14. compute the divergence and curve of a vector field;
15. compute the area of a parametric surface;
16. evaluate surface integrals using Stokes'' Theorem and the
Divergence Theorem; and
17. demonstrate improved algebra and trigonometry skills by
solving
complex calculus problems.
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11. Course Content Outline: (Provides a
comprehensive, sequential outline of the course content,
including all major subject matter and the specific body of
knowledge covered.)
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I. Three Dimensional Analytic Geometry and
Vectors
A. Three-Dimensional Coordinate Systems
B. Vectors
C. Dot Product
D. Cross Product
E. Equations of Lines and Planes
F. Quadric Surfaces
G. Vector Functions and Space Curves
H. Arc Length and Curvature
I. Motion in Space: Velocity and Acceleration
J. Cylindrical and Spherical Coordinates
II. Partial Derivatives
A. Functions of Several Variables
B. Limits and Continuity
C. Partial Derivatives
D. Tangent Planes and Differentials
E. The Chain Rule
F. Directional Derivatives and the Gradient Vector
G. Maximum and Minimum Values
H. Lagrange Multipliers
III. Multiple Integrals
A. Double Integrals over Rectangles
B. Iterated Integrals
C. Double Integrals over General Regions
D. Double Integrals in Polar Coordinates
E. Applications of Double Integrals
F. Surface Area
G. Triple Integrals
H. Triple Integrals in Cylindrical and Spherical Coordinates
I. Change of Variable in Multiple Integrals
IV. Vector Calculus
A. Vector Fields
B. Line Integrals
C. Fundamental Theorem for Line Integrals
D. Greens'' Theorem
E. Curl and Divergence
F. Parametric Surfaces and Their Areas
G. Surface Integrals
H. Stokes'' Theorem
I. The Divergence Theorem
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12. Typical Assignments: (List types of
assignments, including library assignments.)
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a. Reading Assignments: (Submit at least 2
examples)
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b. Writing, Problem Solving or Performance: (Submit at least 2
examples)
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c. Other (Terms projects, research papers,
portfolios, etc.)
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Program title -
TOPS Code:
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Mathematics,
General- 170100
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SECTION D
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General Education Information:
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1. College Associate Degree GE
Applicability:
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Communication
& Analytic Thinking
Math Competency
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2. CSU GE
Applicability (Recommended-requires CSU approval):
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3. IGETC Applicability (Recommended-requires
CSU/UC approval):
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2:
Mathematical Concepts & Quantitative Reasoning
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4. CAN:
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MATH 22
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SECTION E
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Articulation Information: (Required for
Transferable courses only)
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1.
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CSU Transferable.
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UC Transferable.
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CSU/UC major requirement.
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If CSU/UC major requirement, list campus and major.
(Note: Must be lower division)
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2.
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List at least one community college and its comparable
course. If requesting CSU and/or UC transferability
also list a CSU/UC campus and comparable lower division course.
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SECTION F
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Resources:
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Please consider the identified concerns below:
1.
Library: Please identify the implications to the
library
2.
Computer Support Services: Please identify the implications to
Computer Support Services:
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SECTION G
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1. Maximum Class Size
(recommended):
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2. If recommended class size is not standard,
then provide rationale:
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