Mathematics 126 -- Calculus for Social Sciences 2
Exam 2 -- Things to Know
October 19, 2001
General Information
As announced in the course syllabus,
the second full-period exam of the semester will be given
in class on Friday, October 26. As on the first exam, there will
be seven or
eight questions (maybe grouped together) similar to problems
from the problem sets from this part of the course. You may use a graphing
calculator on this exam, but calculators like the TI 89
or 92 with symbolic manipulation are not allowed on this or
any other exam.
If there is interest, we could schedule an evening review
session Tuesday or Wednesday next week. We will discuss
this in class on Friday, 10/19.
One other (unrelated) announcement -- I have to attend a meeting
of the College Finance and Planning Council during our class
time Monday, 10/22. Prof. Catherine Roberts will be "covering"
for me that day.
Material To Know
The exam will cover from
the material on economic applications of integrals from Section 6.7
(just before Exam 1) through the material on solving differential
equations by separation of variables (section 9.2) from class on Friday, 10/19.
You should know the following topics.
- Present and Future Value of income streams -- know how
to compute these with integrals in cases where the rate of
income generation varies with time (not just the "annuity" formulas
on pages 526 and 527, which assume a constant payment in each
time period). The integral(s) might require the technique of integration
by parts to evaluate. The exam will NOT cover the other economic
applications from Section 6.7 because we did not cover them in class.
- Integration By Parts -- Section 7.1
- Integration with a table -- Section 7.2. Some of these
will require some algebra, and/or a preliminary substitution before
the appropriate table entry can be identified. I will make copies of
the table of integrals from the text and distribute them with the
exam sheet.
- Numerical Integration -- Section 7.3. Know how to use the
Trapezoidal and Simpson's Rules to compute approximations to integrals,
also know how to use the ``error bounds'' given in the box on page 576
of the text. (I'll put the formulas from page 576 on the sheet
with the table of integrals, so you won't need to memorize them.)
- Improper Integrals -- Section 7.4
- Differential Equations -- Section 9.1. Know
how to verify that given functions are
solutions of differential equations, general solutions, particular
solutions satisfying given initial conditions.
- Separable Differential Equations -- Section 9.2. Know how
to solve by separation of variables and integration.
Good Review Problems
- Problems like 6.7/9-15
- Problems like 7.1/1-32, 42, 43
- Problems like 7.2/1-30
- Problems like 7.3/1-5, 15-22, 25, 27
- Problems like 7.4/15-25, 50
- Problems like 9.1/1-18, 21
- Problems like 9.2/1-10, 17-25.