> Day 27 in Mat329

Day 27 in Mat329

Last time

Next time

Today:

Announcements
- Your 15.1 homework is returned: Graded 1, 8, 12.
  1. #8: if it asks you to explain something, please explain (don't ignore); half of you are in the "ignore" category...
  2. #12: you were to use geometry to make your life easy. The volume is a wedge, and easy to calculate.
- Your 15.2 homework is not yet returned: Graded 10, 25, 34. (Thanks to Owen Sharp and Michael Mangus for their Mathematica help on #34.)
  Michael Booth took a nice approach to #34.
A comment on separability: Separability of a bivariate function means that you will have two ordinary univariate integrals to do: the second variable will only appear in limits of integration, if at all.
But you can not necessarily write the integral as a product of two integrals (unless the region is rectangular).
Today we'll do a little Mathematica practice for integration.
- The 15.1 homework file I provided has my most general code for doing numerical approximations of integrals via the midpoint method.
  1. Review this code, and try my routine MidpointApprox on exercises 2-4, p. 1005.
  2. Now: those exercises also ask you to use points other than midpoints. How would you adapt MidpointApprox to create UpperRightApprox, LowerRightApprox, and LowerLeftApprox? Try it!
    I have the answers available, so that you can check that you're correct.
- Try some problems from Section 15.3, using RegionPlot.
  1. Draw the regions being integrated over for problems #2-5, p. 1019 (we did exercises 1 and 6 together in class)
  2. Now use RegionPlot to graph the regions, and see if you got them right!
  3. Finally, evaluate the integrals, and see if you're right.
    I have the answers available, so that you can check that you're correct.

Website maintained by Andy Long. Comments appreciated.