1. No category

Course Outline – Seattle Central Community College
Course Prefix & No.:
Title:
MATH&163
Credits:
Calculus 3
Division: Science & Math
Max Class Size:
32
Course length:
11
weeks
Program/Department: Mathematics
Prerequisite(s):
MATH 152 with a grade of 2.0.
Total Contact Hours: 55
Lecture: 55
Lab:
Clinical:
Other:
(11 h. = 1 cr.)
(unsupervised; 33 hrs. = 1 cr.)
Course
Description
Learning
Outcomes
5
Mode(s) of Delivery:
On campus self-contained
Correspondence
Tele-course
Online instruction
Hybrid (e.g., online and on campus)
Other (please describe):
This course extends the concepts and procedures of calculus to functions of more
than one variable. The principal topics covered include vectors and the geometry
of 3 space, vector functions in two and three dimensions, partial derivatives and
multiple integrals. Conceptual understanding and applications are stressed
throughout the course. Technology, including mathematical software capable of
three dimensional graphing, is used where appropriate to support student
learning.
As a result of taking this course, students will be able to:
 demonstrate an understanding of three dimensional coordinate systems
 apply vector algebra to solve problems relating to the equations of lines and
planes
 apply vector concepts of dot and cross product to solve geometric and
applied problems
 solve geometry problems which involve lines and planes in 3 space
 demonstrate an understanding of the algebra and geometry relating to the
quadric surfaces
 derive and use vector functions to solve geometric and applied problems
 calculate derivatives and integrals of vector functions
 analyze the geometry of vector functions using the concepts of arc length
and curvature
 apply calculus concepts and procedures relating to velocity and acceleration
to solve problems relating to motion in space
 derive and analyze functions of several variables and their graphs including
the use of contourplots
 demonstrate an understanding of the concepts of limits and continuity as
they apply to functions of several variables
 calculate partial derivatives
 demonstrate an understanding of the geometric interpretation of partial
derivatives
 apply partial derivatives to solve applied problems
Last Update: 4/14/15
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find the equation of a tangent plane when presented with appropriate
information
apply the chain rule in a multivariable context
calculate directional derivatives and the gradient
demonstrate a conceptual and geometric understanding of the directional
derivative and the gradient
apply appropriate tests to determine optimal values for multivariable
functions.
calculate double integrals over rectangular regions
calculate iterated integrals
calculate double integrals over general regions
solve application problems involving double integrals
Program/Degree
Outcomes
This course addresses the following program or degree outcomes:
 Develop and use skills in critical thinking, quantitative analysis
 Develop and use skills for in-person interactions with individuals and within
groups.
 Use methods and modes of inquiry specific to mathematics
 Demonstrate effective oral and written communication, teamwork and
collaboration in mathematical settings
 Demonstrate academic honesty and ethical behavior
Topical Outline
and/or Major
Divisions
This course covers the following topics:
 Three dimensional coordinate systems
 Vectors
 The Dot Product
 The Cross Product
 Equations of Lines and Planes
 Functions and Surfaces
 Cylindrical and Spherical Coordinates
 Vector Functions and Space Curves
 Derivatives and Integrals of Vector Functions
 Arc Length and Curvature
 Motion in Space: Velocity and Acceleration
 Functions of Several Variables
 Limits and Continuity
 Partial Derivatives
 Tangent Planes and Linear Approximations
 The Chain Rule
 Directional Derivatives and the Gradient Vector
 Maximum and Minimum Values
 Lagrange Multipliers (optional)
 Double Integrals over Rectangles
 Iterated Integrals
Last Update: 4/14/15
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Distribution Area
Double Integrals over General Regions
Applications of Double Integrals
Natural World
Additional
This course requires concurrent enrollment in CSC102Q: Computers in
Information
Mathematics.
CAC Use Only
QSR
IS
C
GS
US
None
Special
Designation (s)
Outline Prepared by: Mike Pepe
Date: November 2, 2011
Last Update: 4/14/15