Oakton College

Generic Course Syllabus

I Course Course Course
Prefix Number Name Credit Lecture Lab
MAT 250 Calculus I 5 5 0
II. Prerequisite
MAT 149 (Elementary Functions, preferred) or both MAT 122 (Trigonometry) and MAT 140 (College Algebra) all with a grade of C or better or appropriate score on the Mathematics Assessment Test.
III. Course (Catalog) Description
This course focuses on limits, continuity, derivatives, indefinite integrals and definite integrals of algebraic, trigonometric, exponential and logarithmic functions, and applications of differentiation and integration.  Use of technology is integrated throughout.
IV. Learning Objectives
A. Understand the concept of limit.
B. Understand the concept of continuity.
C. Understand the concept of derivative.
D. Evaluate derivatives of algebraic, trigonometric, exponential, and logarithmic functions.
E. Use derivatives to solve optimization problems, motion problems, and problems involving rates of change. 
F. Use derivatives to analyze functions and their graphs.
G. Understand the concepts of indefinite integral and definite integral.
H. Evaluate indefinite and definite integrals.
I. Use definite integrals to find area, average functional value, distance traveled, and total change.
J. Use of technology for finding limits, derivatives, and integrals.
V. Academic Integrity
The very nature of higher education requires that students adhere to accepted standards of academic integrity. Therefore Oakton Community College has adopted a Code of Academic Conduct and a Statement of Student Academic Integrity. These may be found in the Student Handbook. You may also find a summary of the Code of Academic Conduct on the College Catalog.  Among the violations of academic integrity listed and defined are: Cheating, plagiarism, falsification and fabrication of records and official documents, personal misrepresentation and proxy, and bribes, favors, and threats.
It is the student's responsibility to be aware of behaviors that constitute academic dishonesty.
Pursuant to the due process guarantees contained in the Policy and Procedures on Student Academic Integrity, the minimum punishment for the first offense for a student found in violation of the standards of academic integrity is failure in the assignment. In addition, 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.
VI. Outline of Topics
1. Functions and Limits
  a. Functions and their graphs
  b. Operations with functions
  c. Limits
  d. Infinity and limits
  e. Continuity
  2. The 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. Higher order derivatives
  f. Implicit differentiation
  g. Linear approximations of functions
3. 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. Graph the derivatives to find local extrema and inflection points
  f. Optimization problems
  g. Rate of change
  h. Newton's Method
4. The Definite Integral
  a. Rectangular and trapezoidal approximations for area undercurve
  b. Sigma notation
  c. Definition and properties of the definite integral
  d. Evaluating of definite integrals
  e. Evaluating antiderivates
f. The Fundamental Theorem of Calculus
  g. Evaluating integrals by substitution
5. Applications of the Definite Integral
  a. Area under curve
  b. Average functional value
  c. Distance and velocity
d. Area between two curves
6. Recommended Technology
  a. Graphically, numericallyand/or symbolically find limits
b. Graphically, numerically and/or symbolically find derivatives
c. Evaluate integrals numerically and/or symbolically

 
 
VII. 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 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.)
IX. Instructional Materials
Thomas' Calculus: Early Transcendentals, 10e by Finney, Weir, & Gordian, Addison-Wesley, 2002
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 completed by instructor.)

Evaluation methods can include grading homework, chapter or major tests, quizzes, individual or group projects, calculator/computer projects and a final examination.
XI. Other Course Information
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 ASSIST office in Instructional Support Services.  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.