MATH241 Fall 2021: Calculus III

Course Information

Instructor: Vesna Stojanoska

Course Webpage: All course details can be found on Moodle and on the instructor's webpage.

Discussion Sections

Section BHD: Tuesday and Thursday 2:00-3:00 PM, 441 Altgeld

Section BHI: Tuesday and Thursday 3:00-4:00 PM, 441 Altgeld

Discussion Notes

Suggestion Form (anonymous Google form, valid until Oct 3)

Intuition and Physical Meaning

Here are some useful links to help you build intuition for the concepts we cover in this course:

• Chain Rule
• Why is arc-length reparametrization an interesting concept to study?
• Lagrange Multiplier
  The Wikipedia page on Lagrange multipliers includes a well-written section on multiple constraints, though this may be beyond the scope of this course. The single constraint section is most relevant.
• Directional Derivatives


• Line Integral
  Check out the two gifs in the vector calculus section for better understanding.
• Change of Variables in Double Integrals:
  • Where does the Jacobian term come from?
  • Illustrations of Change of Variables
  Read the explanations in the first link and consult the second link for illustrations.


• Divergence and Curl of a Vector Field
• Green's Theorem, Divergence Theorem, and Stokes' Theorem
• Relationship Between These Theorems:
  • Green's Theorem and Divergence Theorem: Green's theorem is a 2-dimensional version of the divergence theorem.
  • Green's Theorem and Stokes' Theorem: Green's theorem is a special case of Stokes' theorem.

Extra Fun

• The real shape of Pringles is a hyperbolic paraboloid. :)

• Pringle Ring
• "There's a Delta for Every Epsilon" by Tom Lehrer