Information about Exam II for Math 2443-006H

Mathematics 2443-006H - Honors Calculus IV - Spring 2008

Information about Exam II

Exam II will be in the usual classroom on Thursday, March 13, 2008. It will cover sections 16.2-16.9. There are 52 points possible.

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.

Some of the exam problems will be similar to homework problems, while others will draw upon the material presented in the lectures. As on any exam, it is wise to start with the problems that you feel confident that you know how to do, before moving on to others.

One exam problem will be a repeat of a problem that appeared on Exam I.

The following topics are very likely to appear, although the exam is not necessarily limited to these topics:

  1. Supplying limits of integrals, either double integrals over 2-dimensional domains or triple integrals over 3-dimensional domains.
  2. Using double and triple integrals to find areas and volumes.
  3. Calculating mass and center of mass of 2-dimesional lamina or 3-dimensional solids. This may include finding the centroid, which is the center of mass just taking constant density ρ = 1.
  4. Calculation of surface area using double integrals.
  5. Integration in polar, cylindrical and spherical coordinates.
  6. The Jacobian of a 2-dimensional change of coordinates. The vectors r_u and r_v. Using the Jacobian to calculate integrals using change of coordinates.
You will need to know the formula for dS for a surface that is the graph of a function. You will need to know the formulas x = ρ sin(φ)cos(θ), y = ρ sin(φ)sin(θ), z = ρ cos(θ), and dV = ρ²sin(φ) dρ dφ dθ, for spherical coordinates, and of course the polar coordinate formula dA = r dr dθ. You will need know how to compute moments and center of mass in two and three dimensions.

The following topics do not appear, at least not explicitly: Riemann sums, graphing in polar coordinates, deriving the formulas for x, y, and z in spherical coordinates, graphing in spherical coordinates, Jacobians for 3-dimensional change of coordinate functions.

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. This course varies from semester to semester, so the exams may be quite a bit different from ours.

1. Supplying limits of integrals, either double integrals over 2-dimensional domains or triple integrals over 3-dimensional domains.
2. Using double and triple integrals to find areas and volumes.
3. Calculating mass and center of mass of 2-dimesional lamina or 3-dimensional solids. This may include finding the centroid, which is the center of mass just taking constant density ρ = 1.
4. Calculation of surface area using double integrals.
5. Integration in polar, cylindrical and spherical coordinates.
6. The Jacobian of a 2-dimensional change of coordinates. The vectors r_u and r_v. Using the Jacobian to calculate integrals using change of coordinates.