Calculus III

I.     Course Prefix/Number: MAT 252

       Course Name: Calculus III

       Credits: 4 (4 lecture; 0 lab)

II.    Prerequisite

MAT 251 with a minimum grade of C.

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. Perform and interpret vector operations in space.
  2. Analyze, classify and graph multivariable functions.
  3. Set up and evaluate multivariable integrals.
  4. Evaluate line and surface integrals.
  5. Use technology to perform vector calculations, find partial derivatives, graph surfaces and evaluate relevant integrals.

V.    Academic Integrity and Student Conduct

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.

Please review the Code of Academic Conduct and the Code of Student Conduct, both located online at

VI.   Sequence of Topics

Perform and interpret vector operations in space.

  1. Perform and interpret vector operations in two dimensions.
  2. Perform and interpret vector operations in three dimensions.
  3. Apply the dot product, including in finding the projection of one vector onto another.
  4. Calculate the cross product.
  5. Describe continuous motion by using vector-valued functions.
  6. Differentiate and integrate vector-valued functions.
  7. Solve two- and three-dimensional problems by integrating the equations of motion.
  8. Find the arc length of parametric curves and polar curves.
  9. Find the curvature, principal unit normal vector, torsion and unit binormal vector.
  10. Use technology to make calculations with vectors and differentiate vector quantities.

Analyze, classify and graph multivariable functions.

  1. Graph and analyze equations of plane and surfaces.
  2. Graph and analyze functions of several variables, including the use of contour plots.
  3. Find the limit and continuity of functions in two and three variables.
  4. Calculate partial derivatives.
  5. Apply the chain rule to composite functions involving two or more variables.
  6. Calculate the directional derivative and interpret the gradient geometrically.
  7. Find the equations of a tangent plane explicitly and implicitly and use the equations of a tangent plane for linear approximation.
  8. Solve unconstrained optimization problems using the second derivative test.
  9. Use the method of Lagrange Multipliers for constrained optimization problems.
  10. Use technology graph R3 surfaces and evaluate partial derivatives

Set up and evaluate multivariable integrals.

  1. Set up and evaluate double integrals over rectangular regions.
  2. Set up and evaluate double integrals over general regions.
  3. Set up and evaluate double integrals in polar coordinates.
  4. Set up and evaluate triple integrals in Cartesian coordinates.
  5. Set up and evaluate triple integrals in cylindrical and spherical coordinates.
  6. Set up and evaluate integrals for mass calculations.
  7. Change variables in multiple integrals.
  8. Use technology to evaluate multiple integrals.

Evaluate line and surface integrals.

  1. Analyze properties of a vector field.
  2. Set up an evaluate line integrals.
  3. Determine whether a vector field is conservative and to find a potential function.
  4. Set up and evaluate the circulation and flux forms of Green’s Theorem.
  5. Apply divergence and curl in three dimensions.
  6. Describe surfaces in R3 in two parameters and to derive and evaluate surface integrals of scalar-valued functions and vector fields.
  7. Apply Stokes’ Theorem.
  8. Apply the Divergence Theorem.
  9. Use technology to evaluate line 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 also recommended.  Mathematica, Derive, and TI-92 calculators are available for use at the College at no charge.
Course may be taught as face-to-face, hybrid or online course.

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.  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, calculator/computer projects and a final examination.

The following applies to the online section of this course only:
This online course requires that students take their exams as directed by their instructor: either on campus at Oakton's Testing Center, at an authorized testing center with a face-to-face monitor, or remotely through a pre-approved testing service.   (To be customized by instructor.)

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.

Oakton Community College is committed to maintaining a campus environment emphasizing the dignity and worth of all members of the community, and complies with all federal and state Title IX requirements.

Resources and support for
  • pregnancy-related and parenting accommodations; and
  • victims of sexual misconduct
can be found at

Resources and support for LGBTQ+ students can be found at

Electronic video and/or audio recording is not permitted during class unless the student obtains written permission from the instructor. In cases where recordings are allowed, such content is restricted to personal use only. Any distribution of such recordings is strictly prohibited. Personal use is defined as use by an individual student for the purpose of studying or completing course assignments.

For students who have been approved for audio and/or video recording of lectures and other classroom activities as a reasonable accommodation by Oakton’s Access Disabilities Resource Center (ADRC), applicable federal law requires instructors to permit those recordings. Such recordings are also limited to personal use. Any distribution of such recordings is strictly prohibited.

Violation of this policy will result in disciplinary action through the Code of Student Conduct.