Oakton College

Generic Course Syllabus

I Course Course Course
Prefix Number Name Credit Lecture Lab
MAT 252 Calculus III 4 4 0
II. Prerequisite
MAT 251 (Calculus II) with a grade of C or better.
III. Course (Catalog) Description
This multivariable calculus course focuses on: vectors, functions of several variables, curves and surfaces, differentiation, partial derivatives, multiple integrals, and line integrals.  Use of technology is integrated throughout.
IV. Learning Objectives
A. Perform and analyze vector operations in the plane and in space.
B. Analyze lines, planes and curves in space.
C. Perform calculus operations on curves.
D. Analyze and evaluate multivariable functions.
E. Perform differential calculus operations on multivariable functions.
F. Perform integral calculus operations on multivariable functions.
G. Evaluate line integrals.
H. Use technology for graphing, 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. COURSE OUTLINE
A. Vectors
  1.  Geometric and algebraic review
  2.  Dot product
  3.  Cross product
  4.  Equations of lines and planes in R3
B. Calculus of curves
  1.  Parametric representation of curves in R3
2.  Limits, continuity, and derivatives
3.   Applications including motion, velocity and acceleration
4.   Integration and arc length
5.   Tangent and normal vectors
6.   Curvature
C. Fundamentals of 
multivariable functions
1.  Surfaces
  2.  Contour plots
  3.  Cylindrical and quadratic surfaces
  D. Differential calculus of 
multivariable functions
  1.  Limits and continuity of functions
  2.  Partial derivatives, differentials and the chain rule
  3.  Directional derivatives and gradients
  4.  Tangent planes and normal lines
  5.  Second derivative test and Lagrange multipliers
  6. Applications involving optimization
  E. Integral calculus of 
multivariable functions
  1. The definite integral and Fubini's theorem
  2. Triple integrals in Euclidean coordinates
  3. Cylindrical and spherical coordinates
  4.  Applications including area, volume, average value, centers of mass
  5.  Change in variables and the Jacobian
F. Integrals over curves 
and surfaces
  1.  Line integrals
  2. The Fundamental Theorem of Line Integrals
  3. Div and Curl
  4. Green’s Theorem
  5. Flux and Stoke’s Theorem
  G. Recommended Technology
1. Use of technologyto manipulate vector quantities
  2. Use oftechnology to differentiate vector functions and evaluate integrals.
  3. Use of technology to graph R3 surfaces
  4. Use of technology to evaluate partial derivatives
5. Use of technology to evaluate multiple integrals
  6. Use of technology to evaluate vector quantities and integrals

 
 
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
Calculus, 2nd edition by Bradley and Smith, Prentice-Hall, 1999.
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.