Here are the things you should be able to do on the exam:

• Find critical points of functions of two variables, and determine the nature of the function at each.
• Determine the absolute maximum and absolute minimum, and their locations, of a function of two variables on a bounded region.
• Write a nested sum for approximating an iterated integral of a function of two variables.
• Set up iterated integrals of functions of two variables over rectangular and non-rectangular regions.
• Evaluate iterated integrals of functions of two variables over rectangular and non-rectangular regions.
• Change the order of integration for an iterated integral of a function of two variables.
• Determine whether an iterated integral of a function of two variables can be computed as the product of two integrals.
• Set up and/or evaluate a polar integral of a function of two variables.
• Calculate normal flow through a surface.
• Determine the units for an integral.

• Doing the Exam 3 Preparation Assignment
• Going over Assignments 11, 12, 13, 14, 15, 16, 17. Here are links to the solutions:
  • Assignment 11 Solutions
  • Assignment 12 Solutions
  • Assignment 13 Solutions
  • Assignment 14 Solutions
  • Assignment 15 Solutions
  • Assignment 16 Solutions
  • Assignment 17 Solutions
• Going over the beginning of class exercises on each day from 5/11 through 5/25.

• Find critical points of functions of two variables, and determine the nature of the function at each. Example on page 5 of 5-11 class notes and pages 2-5 of 5-14 class notes. Exercises in all of Assignment 11, Exercise 1 of Assignment 12, Exercise 2 of Assignment 14. 5-14 Class Exercises, answers on pages 2 - 5 of the class notes for 5-14.
• Determine the absolute maximum and absolute minimum, and their locations, of a function of two variables on a bounded region. Example on pages 8 and 9 of 5-14 class notes, given in more detail here. Exercises 2 and 3 of Assignment 12, Exercise 1 of Assignment 14. Page 5 of 5-18 class notes, same as Exercise 3 of Assignment 12.
• Write a nested sum for approximating an iterated integral of a function of two variables. Examples on pages 5 and 6 of the 5-16 class notes, based on the graph on page 2 of the 5-16 class exercises. Example on page 5 of 5-17 class notes, from graph on page 3 of this. Exercise 1 of Assignment 13. Exercise on page 1 of 5-21 class notes, based on graph on 5-21 Class Exercises (answers on page 2 of the 5-21 class notes), Exam 3 Preparation Assignment Exercise 4.
• Set up iterated integrals of functions of two variables over rectangular and non-rectangular regions. Example on page 6 of 5-18 class notes and examples on pages 3 - 6 of 5-21 class notes. Exercises on the iterated integrals setup handout.
• Evaluate iterated integrals of functions of two variables over rectangular and non-rectangular regions. Example on page 7 of 5-16 class notes, and another on page 1 of 5-17 class notes. Example on page 7 of 5-21 class notes. Exercise 2 of Assignment 13, all of Assignment 15, Exercises 1 and 2 of Assignment 16.
• Change the order of integration for an iterated integral of a function of two variables. Example on pages 1 - 3 of 5-23 class notes. Exercises 1(a) and (b) of Assignment 16, Exam 3 Preparation Assignment Exercise 1.
• Determine whether an iterated integral of a function of two variables can be computed as the product of two integrals. Exam 3 Preparation Assignment Exercise 2.
• Set up and/or evaluate a polar integral of a function of two variables. Example on page 7 of 5-23 class notes, pages 1 - 3 of 5-24 class notes. Exercises on the polar integrals setup sheet, Exercise 4 of Assignment 17.
• Calculate normal flow through a surface. Exercise 4 of Assignment 17, Exam 3 Preparation Assignment Exercise 3.
• Determine the units for an integral. Exam 3 Preparation Assignment Exercise 5.