Sec 1.5 The students will probably need some practice with the laws of
exponentials.
Sec 1.6 The students will probably need some practice with the laws of
logarithms.
Sec 3.5 Give a justification of the chain rule.
Sec 5.1 We will only use Riemann sums with right-hand endpoints.
Sec 5.2 Introduce Sigma notation for Riemann sums, but only with equal
subintervals and right-hand endpoints (see the note in Lesson 5)
Sec 5.3 We will use the Euler definition of the integral, which is easier for
the students to use and sufficient for dealing with continuous functions.
See the note in Lesson 5. Spend some time going over this definition in
class.
Sec 5.4 I suggest giving an informal justification of Theorem 4 (without
using the mean value theorem for integrals)
Sec 5.5 Do the integral of tan x as an example in class (it isn't in the book,
although a form of it is in Example 2 of Secion 5.6)
Sec 5.6 Go over the derivation of the formula for the area between curves.
(I put a couple of these derivations on the exam, as a way of encouraging the
students to learn them). I suggest that from this point on the definition of
integral should be given in a more abbreviated form: lim_{\n\to \infty} \sum
f(x_i)\Delta x, (where the sum is from 1 to n, x_i stands for
a+i\frac{b-a}{n}, and \Delta x stands for \frac{b-a}{n}). The book does not
have any examples similar to p. 412 # 59, 60, so you should do one like this
in class. Also note that this kind of problem is a generalization of
problems like Example 8 on page 391.
Sec 6.1 Note that there are two days on this section.
The first day is on the disk method, which is the middle of the section.
Go over the derivation of the formula.
The second day is on the more general volume by slicing method, and also on
the washer method. Again, go over the derivations.