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Mathematics 2934-010 - Differential Calculus III - Fall 2011

Information about the Final Exam

The Final Exam will focus on section 15.6 (the gradient) and 17.1-17.9. It will be in the usual classroom on Monday, December 12 at 1:30. You may work until 3:45, if you wish, which should be plenty of time as many of the problems only require you to set up integrals, not to complete the calculations to evaluate them. Be sure you follow the instructions of each problem, and give the answers requested, without spending time on anything that is not needed.

I expect to post the grades some time on Tuesday. Please check that all scores have been entered correctly on my spreadsheet, and if you wish to contact me about your grade or pick up your final exam, please do so during finals week. I will be traveling during the winter break, and will not be easily accessible after that (I am retiring and moving to Florida--- it's been great working here at OU for the past 33 years but it's time for me to move on in life).

As usual, calculators are not needed, although you may, if you really want to, use a non-graphics simple arithmetic calculator without even trig functions or log and exponential, but no mechanical or electronic device more sophisticated that this (including iPods, earpieces, etc.). Blank paper will be provided, so all you will need is something to write with. Please write your solutions on the blank paper. You may have as many sheets as you need, and may put the problems in any order. Please put your name on your exam paper and all pages of your solutions, and hand them all in together, although without any pages of scratch work that is not to be graded.

Some of the exam questions will be very similar to homework problems or problems from previous quizzes or tests, others will draw upon the material presented in the lectures. Definitions and statements of major theorems are perfectly reasonable questions, and although you do not need to know them word-for-word, you should be able to write down a coherent and accurate definition of any major concept, and state any of the major theorems.

The Final Exam is worth 75 points. The current version has 86 points (which should be helpful). Along with your exam, you will receive a copy of this list of formulas.

Here is an approximate breakdown of the sections of the book that will be directly covered (of course the work in those sections draws on many other sections, for example much of the work in 17.7-17.9 makes use of sections 17.5 and 17.6):

15.6 6
17.3 17
17.4 6
17.5 2
17.6 13
17.7 22
17.8 10
17.9 10
Total 86


The following topics are very likely to appear, although the exam is not limited to them:
  1. The gradient and its fundamental properties (section 15.6).
  2. Vector fields, div and curl.
  3. Line integrals of functions and vector fields. The Fundamental Theorem for Line Integrals.
  4. Conservative vector fields, and the criterion for a planar vector field to be conservative.
  5. Parameterized surfaces. The vectors r_u and r_v and the properties of their cross product. The area element dS and its relation to the area element dR of the parameter domain.
  6. Key examples of parameterized surfaces--- the sphere, the graph of a function, other standard parameterizations.
  7. Surface integrals of functions and vector fields. Major coverage here, be familiar with the basic formulas including the special case of the graph of a function and the sphere case. The formulas list will help, but it is necessary to understand the basic formulas well in order to be able to use them properly.
  8. Green's Theorem, Stokes' Theorem, and the Divergence Theorem, their statements and use. Since we didn't have time to work a lot with Stokes' Theorem and the Divergence Theorem, the problems dealing with them will be straightforward.

The exams from all my classes since 2000 are available at their course web pages, linked at the course pages page.