Information about Exam II for Math 2443-006H

Mathematics 2443-006H - Honors Calculus IV - Spring 2006

Information about Exam II

Exam II will be in the usual classroom on Tuesday, March 28, 2006. It will cover sections 15.7-15.8 and 16.1-16.9.

Calculators or other mechanical assistance are not needed and are not to be used. Blank paper will be provided, so all you will need is something to write with.

The following will definitely be covered, although the exam not necessarily limited to these topics:

  1. Critical points and extreme values of functions of two variables, checking for extreme values on the boundary of a region.
  2. Lagrange multipliers: not much, and no tricky calculations--- just the basic ideas involved in the method.
  3. Riemann sums for functions of two variables, including hands-on calculation for specific functions.
  4. Supplying limits of integration for double and triple integrals, including supplying new limits to change the order of integration.
  5. Polar coordinates will appear extensively, be comfortable with calculation involving polar coordinates.
  6. Calculation of mass using a density function, in two or three dimensions.
  7. Calculation of surface area--- know the formula for dS
  8. Integration in cylindrical and especially in spherical coordinates. Know the formulas for x, y, z, and dV in spherical coordinates, and how to supply limits of integration. Know your way around the hemisphere.
  9. Change of variable: You don't need to memorize the formula for the Jacobian, but be able to use it to change variables in double integrals, as in homework problems.

The following topics do not appear, at least not explicitly: the discriminant D of a critical point of a function of two variables (i. e. the Second Derivative Test), the definitions of Type I and Type II regions, moments and center of mass, derivation of the formulas relating spherical and Cartesian coordinates, intuitive explantion of the formula for dV in polar or spherical coordinates (also these last two are good to have available in your head).

Exams from previous Honors Calculus classes can be found on their course pages (links to them appear on the course pages page). Some were 50-minute classes, but most were 75-minute classes. Of course, these were different classes, so the exams may be quite a bit different.

1.	Critical points and extreme values of functions of two variables, checking for extreme values on the boundary of a region.
2.	Lagrange multipliers: not much, and no tricky calculations--- just the basic ideas involved in the method.
3.	Riemann sums for functions of two variables, including hands-on calculation for specific functions.
4.	Supplying limits of integration for double and triple integrals, including supplying new limits to change the order of integration.
5.	Polar coordinates will appear extensively, be comfortable with calculation involving polar coordinates.
6.	Calculation of mass using a density function, in two or three dimensions.
7.	Calculation of surface area--- know the formula for dS
8.	Integration in cylindrical and especially in spherical coordinates. Know the formulas for x, y, z, and dV in spherical coordinates, and how to supply limits of integration. Know your way around the hemisphere.
9.	Change of variable: You don't need to memorize the formula for the Jacobian, but be able to use it to change variables in double integrals, as in homework problems.