Math 2210 - Calculus III

Here is the list of problems to help you prepare for the final.

• Section 3.5, Numbers 19, 35, 41, 43.
• Section 8.3, Numbers 1, 5, 7, 21, 27, 29, 37, 41.
• Section 8.6, Numbers 1, 5, 7, 23, 25, 33.
• Let f(x,y)=(x^2+3xy,y-x,2xy^2) and g(x,y,z)=(x^2+y^2+z^2,2x/(x+y+z))
  (a) Find the derivative of the composition of f and g at the point (1,1,1)
  (b) Find the derivative of the composition of g and f at the point (1,1).
  

Click here to see a list of all of the Test Questions: Try to redo all of the problems without looking at the answers posted here.

I have decided not to post a sample final (otherwise some people might only study for the topic on the sample final).
Instead, here is a list of all the possible topics on the final (not counting the extra-credit question, which might be on another topic):

• Basic Vector Operations - Sections 3.5 and 8.3.
• Planes & Lines - Section 8.6.
• Limits - Section 9.6.
• Derivatives & Directional Derivatives - Section 9.7.
• Chain Rule - Section 10.2.
• Gradient and Level curves - Section 10.3.
• Max/Min Problems - Sections 10.5 and 10.6.
• Optimization and Optimization with Constraints - Sections 10.5 and 10.7.
• Double Integrals - Section 11.2.
• Triple Integrals - Section 11.5.
• Last Test Stuff - Sections 12.1, 12.2, 12.3, 12.4, 12.5.

Here is the Formula Sheet that you will receive on the day of the test (it is not the final version yet, I might change it when I write the final). If you think that I forgot a formula, please e-mail me before the final.

Last updated on December 8, 2003.