MATH241 Fall 2021: Calculus III

Course Information

Instructor: Vesna Stojanoska

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

Discussion

Section BHD - Tuesday and Thursday 2-3pm, 441 Altgeld

Section BHI - Tuesday and Thursday 3-4pm, 441 Altgeld

Discussion notes

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

Intuition/Physical meaning

Here are some useful links to help you get some intuitions.

• Chain rule
• Why would arclength reparametrization be an interesting object to study?
• Lagrange multiplier
  The above is the Wikipedia page about the Lagrange multiplier. I find the section regarding multiple constraints very well-written, though it might be beyond the scope of this course. I link you to the single constraint section and you can scroll down to see what we can do for multiple constraints.
• Directional derivatives


• Line integral
  The above is the Wikipedia page about line integrals. Take a look at the two gifs in the vector calculus section.
• Change of variables in double integrals
  • Where does the Jacobian term come from?
  • Another page with illustrations
  I would suggest reading explanations in the first link and consulting illustrations in the second.


• Divergence and curl of a vector field
• Green's theorem, the divergence theorem and Stokes' theorem
• Relationship between these theorems
  • Relationship between Green's theorem and the divergence theorem :
    Green's theorem is a 2-dim divergence theorem.
  • Relationship between Green's theorem and Stokes' theorem :
    Green's theorem is a specical case of Stokes' theorem.

Extra fun

• The real shape of pringles is hyperbolic paraboloid. :)

• Pringle ring
• "There's a delta for every epsilon" Words and music by Tom Lehrer