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
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17.3 | 17
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17.4 | 6
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17.5 | 2
|
17.6 | 13
|
17.7 | 22
|
17.8 | 10
|
17.9 | 10
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Total | 86
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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).
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2. Vector fields, div and curl.
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3. Line integrals of functions and vector
fields. The Fundamental Theorem for Line Integrals.
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4. Conservative vector fields, and the
criterion for a planar vector field to be conservative.
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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.
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6. Key examples of parameterized
surfaces--- the sphere, the graph of a function, other standard
parameterizations.
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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.
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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.
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The exams from all my classes
since 2000 are available at their course web pages, linked at the
course
pages page.