- Did I forget to mention the 1000 extra credit points for attending
the picnic? Sorry about that...
- First Exam Tomorrow! It will cover chapter 7 material (and
Newton's method)
- Section 7.8 homework are due today.
I know that this is right before the exam. If there are any you're having particular trouble with, you'll want to ask.
- Homework 7.4 and 7.7:
- 7.4: Graded #25
- In general, if these problems look like they've been copied from the back of the book, you won't get full credit.
- Show work
- Elaborate
- 7.7: Graded #62
- Make sure that you understand which variable we're differentiating wrt (with respect to).
- Part a: wrt T
- Part b: wrt r
- Even if you struggle with part a, you can try part b! Never give up....
- Way too many people didn't hand in their written work....
- If I ask you to hand in written work, it's going to count for half of your assignment (the on-line will be the other half). All homework assignments will eventually be worth the same: 4 points each.
- 7.4: Graded #25
- Just for fun: more weird connections (extreme math):
The Prime Number Theorem: as n goes to infinity, the number of prime numbers less than or equal to n approaches n/ln(n).
Conjectured by Gauss and Legendre; proven by Hadamard and de la Vallee.
- First of all, the big picture: integration by parts is just the
product rule backwards. This integration technique, like all
integration techniques, is really just a differentiation technique in
reverse.
Example: Exercise #2, p. 428
- Integration by parts may need to be carried out multiple times:
sometimes the idea is to simplify the integral each time, until a
really simple one arises allowing us to calculate the final solution
(e.g. Example 4, p. 425). Sometimes it's something of a trick: we
compute the integral multiple times in order to return to the original
integral, allowing us to solve an equation for the original integral
(e.g. Example 5, p. 426).
Example: Exercise #18, p. 428
- Suggested strategy:
- Choose u so that u' is simpler than u itself.
- Choose v' so that
can be evaluated.
- Sometimes v'=1 is a good choice.
Example: Exercise #25, p. 428
- Of course, all this works with definite integrals:
Example: Exercise #49, p. 428