Day 31 in Mat329

Last time

Next time

Today:

Announcements
- We have an exam Thursday, which will cover 14.6 (directional derivatives) through 15.3 (not including 15.4 -- double integrals in polar coordinates -- by the way, your homework is due today!).
  Here is last semester's second exam. (Problem 5 would be considered a triple integral, and wouldn't appear on your exam).
  Here's a Mathematica Key for the exam
- Department chair Prof. Roger Zarnowski is taking the reins today, to work through some triple integrals with you.
- I'll be available most of tomorrow, if you want to stop by to ask questions. I'll be around some of today (although my daughter is visiting NKU today, so I'll want to catch up with her on a tour or two). Come give blood at the ballroom at 3:00 if you want my full attention for an hour!
- Let me know if you need to see me to discuss anything. Contact me via email to set up a meeting.
Last time we began section 15.7: triple integrals, by working #9 carefully.
- We're stepping up the dimension -- no big deal, but we've got more work to do. Sometimes it's just three times as much work (as when we have a separable function, a product of three functions $f(x)g(y)h(z)$).
  The volume element in rectangular coordinates is $dV=dxdydz$, as expected: an infinitesimal box.
- Examples:
  - What's the average temperature in a special empty rectangular room, where
    - Walls are perfectly insulated
    - Floor is kept at constant temperature of 77 degrees F.
    - Ceiling (10 feet above) is kept at constant temperature of 70 degrees F.
    - Temperature equilibrates (is steady in time)
  - #9, p. 1049
  - #20, p. 1049 (this is a volume of rotation from your univariate calculus days -- you might try using disks or shells to find the volume "the old fashioned way".)
  - #33, p. 1050 (writing the integral in different ways)
  - #24, p. 1049
  - Some applications from physics and stats:
    - #49
    - #52 (separable)

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