Mathematics 2433-007 - Calculus III - Fall 2002
Information about the Final Exam
The Final Exam will be in the usual classroom on Tuesday, December 17,
2002. It is scheduled for 1:30 to 3:30, but you may work until 3:45 if you
need the extra time. As usual, take alternate seats.
As usual, only basic, non-graphing calculators may be used (preferably, as
a paperweight), and scratch paper will be available if needed.
The exam will be worth 77 points, and will cover the sections shown in the
following table, which gives the approximate point breakdown of the final
exam questions:
| 11.1 | 6
|
| 11.4 | 5
|
| 12.2 | 5
|
| 12.3 | 3
|
| 12.4 | 3
|
| 12.6 | 6
|
| 12.8 | 4
|
| 12.10 | 10
|
| 13.3 | 2
|
| 13.4 | 2
|
| 13.5 | 5
|
| 14.2 | 9
|
| 14.3 | 13
|
| 14.4 | 4
|
| Total | 77
|
The following topics will definitely be covered, although the exam is not limited to
these topics:
| 1.
| writing parametric equations for circles and graphs of
functions in the plane
|
| 2.
| graphing polar equations in the xy-plane
|
| 3.
| precise mathematical definition of convergence of a
series, meaning of the partial sums s_n, meaning of absolute convergence
|
| 4.
| geometric series and p-series, standard tests for convergence
of series such as comparison, root, ratio tests
|
| 5.
| power series, definition and possible convergence behaviors
|
| 6.
| Maclaurin and Taylor series
|
| 7.
| velocity vector, unit tangent and normal vectors,
tangential and normal components
|
| 8.
| arclength, reparameterization by arclength
|
| 9.
| curvature, its meaning and calculation
|
You should know the following from memory: definition and convergence
behavior of geometric series and p-series, Maclaurin series for e^x,
sin(x), cos(x), and ln(1+x), general formula for the Taylor series at x=a,
equations for lines and planes in 3-dimensional space. You do not need to
know formulas for curvature or for tangential and normal components, but it
will be useful to be familiar with the standard formulas for these and to
be experienced in their use.
The following topics are not covered on the final exam: quadric surfaces,
cylindrical and spherical coordinates.