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Mathematics 2433-001H - Honors Calculus III - Fall 2005

Information about Final Exam

The Final Exam will be in the usual classroom on Thursday, December 15, 1:30-3:30 p. m. You can work until 3:45, so although the exam is somewhat long, there should be ample time to complete it without hurrying.

I hope to post the final grades on our website some time on Friday, and will definitely post them no later than Saturday.

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. As usual, give brief, clear solutions without unnecessary explanation.

A few questions will be very similar to questions from our three in-class exams, so a good way to get started on your preparation is to make sure that you understand the questions from the in-class exams and their solutions.

Here is an approximate point breakdown of the final exam. It is not all that meaningful, since problems in one section use methods and ideas from others that may not even be listed here, but at least it indicates the general emphases of the exam.

11.4 4
12.1 8
12.2 3
12.4 3
12.6 6
12.8 6
12.9 9
13.5 6
13.6 8
13.7 11
14.1 4
14.3 12
 Total 80

  1. For quadric surfaces, you do not need to memorize the different kinds of surfaces and equations. Be able to graph the traces and work out the three-dimensional graph of a quadric surface from them.
  2. There is a fair amount on power series, but not Taylor's theorem and the error of polynomial approximation. The emphasis is more on understanding convergence, convergence tests, and using power series to do things.
  3. The questions on cylindrical and spherical coordinates will emphasize graphing. Understand well the geometric meaning of each kind of coordinate.
  4. For vector-valued functions, the emphasis will be on computation. You need to know how to compute the velocity, acceleration, unit tangent, normal, and unit normal vectors. You should understand curvature and the different ways it can be computed, but do not have to memorize the formulas for computing it.
  5. Know the various convergence tests for series--- comparison, alternating series test, ratio test, etc.
  6. Although the table above does not list questions from sections 13.1-13.4, you need to understand dot and cross product and be able to compute them (especially cross product) in order to work with vector functions, equations of lines and planes, and so on.