Vector Calculus (MATH 223)

We offer an optional 1-unit supplementary instruction course, Math 196V, to accompany Math 223. This course develops problem-solving skills in a hands-on learning environment. Enroll now!


The Math Department offers free walk-in tutoring for Math 223 in the Math Teaching Lab room 121, Monday-Friday starting next Monday. Click here to see the schedule starting January 14.


Upon successful completion of this course, the student will be able to:

  • Recognize and sketch surfaces in three-dimensional space;
  • Recognize and apply the algebraic and geometric properties of vectors and vector functions in two and three dimensions;
  • Compute dot products and cross products and interpret their geometric meaning;
  • Compute partial derivatives of functions of several variables and explain their meaning;
  • Compute directional derivatives and gradients of scalar functions and explain their meaning;
  • Compute and classify the critical points;
  • Parameterize curves in 2- and 3-space;
  • Set up and evaluate double and triple integrals using a variety of coordinate systems;
  • Evaluate integrals through scalar or vector fields and explain some physical interpretation of these integrals;
  • Recognize and apply Fundamental theorem of line integrals, Green’s theorem, Divergence Theorem, and Stokes’ theorem correctly.


Section information and links to instructor class webpages are found here.

MATH 223 (4 credits)

MATH 196V (1 unit)


A graphing calculator is required for Math 129. We recommend any model in the TI-83 or TI-84 series. Students are not allowed to share calculators during exams and quizzes.


Math 223 uses a computer grading program called WebAssign for textbook assignments. Logging into WebAssign can only be done through the WebAssign Login link in your Math 223 D2L site.

Additional homework and/or quizzes may be assigned by instructors. Be sure to check with your instructor.

Things to Know About WebAssign at the UA

Written Homework


Math 223 covers chapters 12 - 20 of Multivariable Calculus; 6th edition; McCallum, Hughes-Hallett, Gleason, et al.; Wiley.

The Textbook and WebAssign access for homework are being delivered digitally via D2L through the Inclusive Access program.

Inclusive Access Deadlines and Procedures

Inclusive Access FAQs


These calendars are to be used as guidelines. Individual course sections may deviate from the suggested calendar. Be sure to check with your instructor.

Math 223 - MTWR


A common comprehensive final exam is given in all sections of Math 223 on Tuesday, December 11 from 1:00 - 3:00 pm.

Final Exam Information (coming soon)

Final Exam Locations

Study Guide (updated), Answers

Final Exam Fall 2012, Answers

Final Exam Spring 2012


Math Department Tutoring

Precalculus Review (University of MI)


Calculus Videos (Khan Academy)


Calculator Programs

Math 223 demonstrations (Wolfram Project)

Dot Product (Paul Falstad)

Cross Product (Syracuse University)

Plotting surfaces and contours (Kaskosz & Ensley)

Plotting (MIT Open Courseware)

Surfaces (JavaView)

Vector Field Analyzer (Matthias Kawski - ASU)

3-D Vector Field Applet (Paul Falstad)

3-D Vector Fields (OR State University)