Math 32L (Calculus II)
Sections 5 and 6
Fall 1996
Plan for Week 4
This week completes the development started in Week 3 of the concept
of the (definite) integral. We first establish a connection (part
of the Fundamental Theorem of Calculus) between the concepts of integral
and derivative. This connection gives new importance to the idea of antiderivative,
which we give a new name and notation to associate it with the definite
integral. From our Euler's Method development of the Fundamental Theorem
we see that the same argument leads to the other half of the theorem —
a new derivative formula for functions defined by integration to a variable
upper limit.
We start the week with a project that picks up on Lab 6 and the velocity-squared
model for air resistance: Sky Diving. In the lab we were limited to an
approximate solution via Euler's Method. Here we take up the symbolic solution.
Here is this week's part of the syllabus:
Day Topic Reading Activity
9/23 Fundamental Theorem (Evaluation) 8.2 Sky diving project
9/25 Indefinite integral 8.3
9/26 Lab 16: Area from Sums
9/27 Fundamental Theorem (Antiderivatives) 8.4
Observations:
- As a general rule, you are expected to read the relevant section of
the text before the class period on using it.
- Always attempt to do all Exploration Activities and Checkpoints
as you come to them in the reading. (The EA's will work better if you are
reading with a study group and discussing the ideas.) These will not be
included in problems assigned to be turned in, but they may be the basis
for unannounced quizzes in class. If you have worked them out, you can
respond to an open-book quiz by copying the work already done. If you skipped
over them, you probably won't be able to answer them in the short time
allowed for a quiz.
- Your next homework papers will be turned in on Monday, September 30.
Those papers should include solutions to the problems whose numbers are
boldfaced in the assignment below. The assignment dates are start
dates.
Assignments
- Monday, Sep. 23, Sec. 8.2/#1, 3, 5, 7, 9, 13, 17, 19, 21, 23, 25, 27,
31, 35, 37, 39, 41, 43, 45, 49, 53, 55; pp. 457-458, #20,
22, 32
- Wednesday, Sep. 25, Sec. 8.3/#3, 7, 11, 15, 18, 22, 26, 30, 33, 37,
41, 45; pp. 458-459, #24, 26, 35
- Friday, Sep. 27, Sec. 8.4/#1, 5, 7, 11, 15, 19, 23, 27,
31, 32, 33, 34
David A. Smith <das@math.duke.edu>
Last modified: September 20, 1996