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GENERIC COURSE SYLLABUS
I. Course Course Course
Prefix Number Name Credit Lecture Lab
MAT 250 Calculus
I 5 5 0
II. Prerequisites:
MAT 149 or both MAT 140 and MAT 122,
all with grades of C or better, or an appropriate score on the OCC Mathematics
Assessment Test.
III. Course (Catalog) Description:
Course is
first in calculus and analytic geometry. Content focuses on limits, continuity,
derivatives, indefinite integrals and definite integrals, applied to algebraic,
trigonometric, exponential and logarithmic functions, and applications of
differentiation and integration. Technology integrated throughout course.
IV. Course Objectives:
A. Demonstrate
and apply an understanding of the concept of limits by calculating and
algebraically manipulating limits of algebraic and transcendental functions.
B. Demonstrate
and apply an understanding of the concept of continuity by classifying
functions as continuous or discontinuous at points and on intervals.
C. Demonstrate and apply an understanding
of the concept of the derivative by calculating limits of difference quotients, and using
slopes of tangent lines to calculate the rate of change of functions.
D. Evaluate
derivatives of algebraic, trigonometric, exponential, and logarithmic
functions, and derivatives of functions defined by parametric equations.
E. Use
derivatives to solve optimization problems, motion problems, and problems
involving rates of change.
F. Use derivatives to analyze functions
and their graphs, extrema and inflection points.
G. Demonstrate and apply an understanding
of the concepts of indefinite and definite integrals by calculating
antiderivatives of functions given as rates of change.
H. Calculate
and evaluate indefinite and definite integrals.
I. Use
definite integrals to find area, average functional value, distance traveled,
and total change.
J. Use
technology to solve calculus problems involving limits, derivatives, and
integrals.
V. Academic Integrity:
Students and employees at
·
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:
A. Functions
and Limits
a. Functions and their graphs
b. Operations with functions
c. Limits
d. Limits at infinity
e. Continuity
B. Derivative
a. Definition of the derivative
b.
Differentiation
rules for sums, products and quotients of functions
c.
Algebraic,
trigonometric, exponential and logarithmic functions and their derivatives
d.
The
Chain Rule
e.
Parametric
equations and their derivatives
f. Higher
order derivatives
g. Implicit differentiation
h. Linear approximations of functions
C. Applications
of the Derivative
a. Local extrema of functions
b. Increasing/decreasing functions and the
first derivative
c. Concavity and the second derivative
d.
Curve
sketching
e.
Graphing
derivatives to find local extrema and inflection points
f. Optimization problems
g. Rates of change
h.
D. Definite
Integral
a. Rectangular and trapezoidal
approximations for area under curve
b. Sigma notation
c. Definition and properties of the
definite integral
d. Evaluating of definite integrals
e. Evaluating antiderivatives
f.
The
Fundamental Theorem of Calculus
g. Evaluating integrals by substitution
E. Applications
of the Definite Integral
a. Area under a curve
b. Average functional value
c. Distance and velocity
d.
Area
between two curves
F. Recommended Technology
a. Graphically,
numerically and/or symbolically find limits
b.
Graphically,
numerically and/or symbolically find derivatives
c.
Evaluate
integrals numerically and/or symbolically
Note:
L’Hopital’s Rule in Chapter 4 of Thomas is not to be covered in MAT 250.
It is covered in MAT 251.
VII. Methods of Instruction:
(To be completed by instructor.)
Methods of presentation can include lectures,
discussion, demonstration, experimentation, audio-visual aids, group work, and
regularly assigned homework.
Calculators/computers will be used when appropriate. Use of a computer algebra system is
recommended. Mathematica is available for use at the College at no charge.
VIII. Course Practices Required:
(To be completed by
instructor.)
IX. Instructional Materials:
Required
Textbook: http://www.oakton.edu/acad/dept/mcs/mat/textbooks.htm
Required
Materials: A TI-83 graphics calculator
(or an equivalent or more advanced model).
A graphics
calculator is required. A TI-83 or
higher numbered model will be used for instructional purposes.
X. 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,
computer/calculator projects, and a final examination.
XI. Other 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 ASSIST office in the
Effective beginning term Fall
2009 Ending term
Syllabus prepared by: J.Strehler, P.Boisvert, M. Farquhar, J.
Kotowski, G. McClarren,
K. Murashkina, S. Hamed Date: May 2009
Reviewed by Dept/Program Chair: J. Hassett Date: May 2009____
Approved by Dean: R. Sompolski Date: May
2009__________