- Did anyone forget that the departmental picnic is coming up?
It's this Sunday, starting at 4:30 pm, at Highlands Park in Fort Thomas.
You're free to just show up, but if you'd like to make a reservation, email me, or sign up on Brooke Buckley's door (across from the Student Lounge upstairs).
- First Exam: Tuesday, will cover chapter 7 material (and
Newton's method)
- Section 7.7 problems are due today.
- Section 7.8 homework is due Monday, 9/22.
I know that this is right before the exam. If there are any you're having particular trouble with, you'll want to ask about those Monday.
- The 8.1 homework is on-line.
- Section 8.2 homework: Hand these in (not on-line): pp. 428-429, #4, 5, 8, 15, 16, 23, 36, 50, 66, 69. Due Monday, 9/29.
- Let's review #56....
- 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