OAKTON COMMUNITY COLLEGE
GENERIC COURSE SYLLABUS
I.
II.
Course
Prefix
Course
Number
Course
Name
MAT
252
Calculus III
Credit
4
Lecture Lab
4
0
Prerequisite:
MAT 251 with a grade of C or better.
III.
Course (Catalog) Description:
Course surveys topics of calculus for multivariable functions. Content focus is on: vectors,
functions of several variables, curves and surfaces, differentiation, partial derivatives, multiple
integrals, and line integrals. Technology is integrated throughout.
IV.
Learning Objectives:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
V.
Perform and interpret vector operations in space, including dot and cross products.
Use vectors to represent and analyze lines, planes and curves in space.
Differentiate and integrate curves in space
Use tangent and normal vectors to analyze motion along curves in space.
Analyze, classify and evaluate multivariable functions.
Use differential calculus operations, including partial derivatives and gradients,
to calculate tangent planes and normal lines for multivariable functions.
Solve applications of optimization for multivariable functions, including Lagrange
multipliers.
Use multiple integration to solve applications, including area, voluem, and center of mass.
Model and solve problems using cylindrical and spherical coordinates.
Evaluate line, curve and surface integrals.
Use technology to graph, differentiate, and integrate multivariable functions.
Academic Integrity:
Students and employees at Oakton Community College are required to demonstrate academic
integrity and follow Oakton’s Code of Academic Conduct. This code prohibits:




cheating,
plagiarism (turning in work not written by you, or lacking proper citation),
falsification and fabrication (lying or distorting the truth),
helping others to cheat,




unauthorized changes on official documents,
pretending to be someone else or having someone else pretend to be you,
making or accepting bribes, special favors, or threats, and
any other behavior that violates academic integrity.
There are serious consequences to violations of the academic integrity policy. Oakton’s policies
and procedures provide students a fair hearing if a complaint is made against you. If you are
found to have violated the policy, the minimum penalty is failure on the assignment and, a
disciplinary record will be established and kept on file in the office of the Vice President for
Student Affairs for a period of 3 years.
Details of the Code of Academic Conduct can be found in the Student Handbook.
VI.
Outline of Topics:
1.
Vectors
a.
b.
c.
d.
Geometric and algebraic review
Dot product
Cross product
Equations of lines and planes in R3
2.
Calculus of curves
a.
Parametric representation of curves in R3
b.
Limits, continuity, and derivatives
c.
Applications including motion, velocity, and acceleration
d.
Integration and arc length
e.
Tangent and normal vectors
f.
Curvature
3.
Fundamentals of multivariable functions
a.
Surfaces
b.
Contour plots
c.
Cylindrical and quadratic surfaces
4.
Differential calculus of multivariable functions
a.
Limits and continuity of functions
b.
Partial derivatives, differentials and the chain rule
c.
Directional derivatives and gradients
d.
Tangent planes and normal lines
e.
Second derivative test and Lagrange multipliers
f.
Applications involving optimization
5.
Integral calculus of multivariable functions
a.
The definite integral and Fubini's theorem
b.
Triple integrals in Euclidean coordinates
c.
d.
e.
VII.
Cylindrical and spherical coordinates
Applications including area, volume, average value, centers of mass
Change in variables and the Jacobian
6.
Integrals over curves and surfaces
a.
Line integrals
b.
The Fundamental Theorem of Line Integrals
c.
Div and Curl
d.
Green’s Theorem
e.
Flux and Stoke’s Theorem
7.
Recommended Technology
a.
Use of technology to manipulate vector quantities
b.
Use of technology to differentiate vector functions and evaluate integrals.
c.
Use of technology to graph R3 surfaces
d.
Use of technology to evaluate partial derivatives
f.
Use of technology to evaluate multiple integrals
g.
Use of technology to evaluate vector quantities and integrals
Methods of Instruction:
(To be completed by instructor)
Methods of presentation can include lectures, discussion, experimentation, audio-visual aids,
small-group work and regularly assigned homework. Calculators/computers will be used when
appropriate. Use of a computer algebra system is also recommended. Mathematica, Derive, and
TI-92 calculators are available for use at the College at no charge.
VIII.
Course Practices Required:
(To be completed by instructor)
Course may be taught as face-to-face, media-based, hybrid or online course.
IX.
Instructional Materials:
Note: Current textbook information for each course and section is available on Oakton's
Schedule of Classes. Within the Schedule of Classes, textbooks can be found by clicking on an
individual course section and looking for the words "View Book Information".
Textbooks can also be found at our Mathematics Textbooks page.
A graphics calculator is required.
instructional purposes.
X.
A TI-83 or higher numbered model will be used for
Methods of Evaluating Student Progress:
(To be determined and announced by the instructor)
Evaluation methods can include graded homework, chapter or major tests, quizzes, individual or
group projects, calculator/computer projects and a final examination.
XI.
Other Course Information:
If you have a documented learning, psychological, or physical disability you may be entitled to
reasonable academic accommodations or services. . To request accommodations or services,
contact the Access and Disability Resource Center at the Des Plaines or Skokie campus. All
students are expected to fulfill essential course requirements. The College will not waive any
essential skill or requirement of a course or degree program.
________________________________________________________________________________
Effective beginning term: Fall 2014
(term) (year)
Ending term ___________
(term) (year)
Syllabus prepared by: 2013-14 Math Syllabus Committee
(chair: P. Boisvert)
Date
Mar 2014
Reviewed by Dept/Program Chair: J. Hassett
Date
Mar 2014
Approved by Dean: R. Sompolski
Date
Mar 2014