- First Exam:
- Coming up next Tuesday: Exam 1. Because of our power
problem, I suggest one of two paths:
- The exam will only cover chapter 7 material (and Newton's method)
- We move it to Thursday, and include section 8.1.
- Coming up next Tuesday: Exam 1. Because of our power
problem, I suggest one of two paths:
- I'm sorry that I wasn't able to check over your section 7.3 problems due to the power situation. I'm doing that now. For the moment, I'll ask you to hand in your 7.4 work (including by hand) on Thursday (I'm sure that you may have had power issues, too).
- Extended due date: Section 7.8 homework:
pp. 397-399, #1, 2, 6, 10, 17, 18, 21, 57 will be done
on-line; problems 50, 83, and 84 will be handed in separately. Due Monday, 9/22.
- Hold the pitch-forks!
- For example, the sine function has inverse function
arcsin (note the bad notation below -- don't be confused! But our notation in mathematics is sometimes "context sensitive"):
and cosine function has inverse function arccos:
- Arctan and arccot are also sometimes useful:
- Derivatives: They're computed in the usual "sneaky" inverse function way:
Exercise 49, p. 398
- Examples:
- #50, p. 398
- #85, p. 399
- 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
- #20, p. 421
- 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.