Study Guide 1 
(Math 2423, Calculus III-B, Section 002, Fall 2000)

Homework

Read sections 12.7, 13.1, and 13.2, and work the following problems for the quiz on Tuesday, October 24. YOU MUST WORK ALL PROBLEMS!! However, you only need to turn in the problems marked by an asterisk. These are due Tues. Oct. 24 at the beginning of class.

Key Skills :

  1. Find a unit normal vector to a surface (just calculate the "Big" gradient vector, and normalize). (12.7: 5,9)
  2. Find an equation for the tangent plane to a surface at a given point. (key idea: for any vector parallel to the plane, the dot product with gradient vector must be zero) (12.7: 11, 16 )
  3. Find parametric or symmetric equations for the normal line to a surface. (just find the line parallel to the unit normal vector) (12.7: 27)
  4. Calculate the integral with respect to a single variable of a function of several variables (13.1: 5,7)
  5. Evaluate an iterated integral (13.1: 14, 24, 13.2:9)
  6. Switch the order of integration for an iterated integral (this is trickier than you might think, so be sure to graph the region of integration!!) (13.1: 26, 27)
  7. Find the area of a region using an iterated integral (13.1: 41)
  8. Switch the order of integration to integrate a function that can't be integrated with the original order. (13.1: 52)
  9. Evaluate a double integral by setting up an iterated integral (13.2: 13, 18,23)
  10. Calculate the volume of a solid region (13.2: 18,23,26,28,39)