- First Exam: Tuesday, will cover chapter 7 material (and
Newton's method)
- I've graded your section 7.3 problems. You may find some comments in the "gradebook" of IMathAS. There were lots of little problems to clean up (students who knew what they were doing, but couldn't get the software to understand). Thanks for the written work - that helped at times.
The main thing I'm after is that you try the problems!
- Section 7.4 problems are due today; 7.7 tomorrow.
- 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.
- I'll be putting the 8.1 homework on line right after class today.
- There are various schemes for numerical integration:
- Left Rectangular
- Right Rectangular
- Midpoint
- Trapezoidal
- Simpson's rule.
- Three of the rules are so called "rectangle rules" (LRR, RRR, Midpoint Rule);
but as the image to the right (above) and the graphical insight on p. 415 show, we can think of the Midpoint rule as being a "Tangent rule":
- The Trapezoidal rule is really just the average of the LRR and RRRs.
- Simpson's rule is a "blend" of the Midpoint and Trapezoidal rules, which
perfectly balances the errors of the two to generate a better rule:
- Examples:
- #9, p. 421, with all gory details.
- #20, p. 421, with all gory details.
- Let's get started on #56....
- Links:
- Here's a nice summary of the issue, focused on the use of Mathematica to illustrate them. Interesting even if you don't use Mathematica.