Here is a brief summary of what we did in the first week:
1. We covered section 4.9. Make sure to start making your notesheet. Anything you can’t quite remember from table 2 on page 341 put it on your sheet! That table is your best friend.
2. We covered 5.1. The important part of this section is to understand the idea of cutting the region up into strips and add the areas of the approximate rectangles. Think about the idea behind taking limit, compare it with how you computed tangent lines from secant lines (also a limiting process!) Don’t get scared about the limits and sums, but do come and talk to me if you have trouble with them.
Lastly, one hint on problem 34 in section 4.9. The derivative is only first order, but two conditions are given. That is because the antiderivative of 1/x is ln|x|, which is a multi-part function. For positive x, there is a constant C_1, which you can compute from f(1); for negative x, there is a constant C_2, which you can compute from f(-1).
If you have any question or comments of the class, let me know! Have a nice weekend!
Hope your first weekend was good! Here is a brief preview for the second week:
We will continue finish the problems from 5.1 on Tuesday, then move to 5.2. Then we will discuss 5.3 on Thursday. Remind you: homework one is due next Thursday, so do take advantage of the office hours and homework sessions Tuesday-Thursday!
Tuesday: 5.2. You will finally see definite integrals! We will introduce them, and talk about their properties.
Thursday: 5.2, 5.3. We will discuss the fundamental theorem of calculus.
Alright, see you on Tuesday!
Homework problems due on Friday:
Make sure you start early!