Mathematics 2423-001H - Honors Calculus II - Spring 2005
Information about the Final Exam
The information given here is subject to (minor) change, so check back
periodically.
I will have special office
hours during finals week.
Calculators are not needed and are not to be used. Blank paper will be
provided, so all you will need is something to write with. You will be
given a copy of the following table of
integrals, which you can and should use whenever possible. Note that it
also includes some basic information about Simpson's rule.
The exam will be rather focused on certain topics, as indicated in the
following description. It will be similar to the in-class exams, although
longer. As usual, avoid spending a lot of time on any individual problem
unless you have completed all the other problems that you definitely know
how to do. Grab easy points first.
Here is an approximate point breakdown by sections of the text. Be aware
that quite a bit of material from other sections may appear. For example,
even though there is not much point value assigned to the sections on
exponentials and logarithms, you need to know these functions well in order
to solve problems from other sections. Also, some sections with only a few
points shown in the table may be needed for later sections. For example,
the differential of arclength, studied in section 9.1, is used in all
calculations of surface area in section 9.2.
| 5.2 | 13
|
| 5.3 | 10
|
| 6.2 | 3
|
| 7.1 | 19
|
| 7.6 | 4
|
| 7.7 | 8
|
| 8.1 | 14
|
| 8.3 | 6
|
| 8.4 | 6
|
| 8.6 | 6
|
| 8.7 | 8
|
| 8.8 | 8
|
| 9.1 | 2
|
| 9.2 | 9
|
| Total | 116
|
Here are the topics that receive particular emphasis. Of course, the exam
is by no means limited to these topics:
| 1.
| Riemann sums and the definition of the integral. Be able to
work with explicit partitions and Riemann sums, know the typical choices of
sample points such as left-hand endpoints and right-hand endpoints.
|
| 2.
| Inverse functions: general concepts, how the domains and
ranges work, the definition of one-to-one function, the inverse sine and
inverse tangent functions.
|
| 3.
| Integration by parts, and the other major techniques of
integration.
|
| 4.
| The material in sections 8.7, 8.8, 9.1, and 9.2 will
receive some extra coverage, since it has not already appeared on the
in-class exams.
|
You should know the standard trig identities including the ones to express
sin2(x) and cos2(x) in terms of cos(2x). You do not
need to know the identities for simplifying expressions of the form sin(A)cos(B),
sin(A)sin(B), or cos(A)cos(B).
Among the topics that do not appear on the Final Exam are: telescoping
sums, formulas for summing powers of n, the distance problem, the Mean
Value Theorem for Integrals, complicated volume problems, optimization or
related rates word problems, inverse hyperbolic trig functions.