Day 41 in Mat360

Today:

• Announcements:
  • Repair those in-class Exam IIs for some credit back.

  • Returned:
    • Quiz over 4.4
      • Some of you tried to rederive the composite rule from the elemental rule -- you can, but it's a lot uglier than simply remembering the 1-4-2-4-2-step.
      • Alternatively, use
      • In the end, you need to use your head! Look at the data:
        1. What's a rough average value?
        2. What's the width of the interval?
        3. What's a rough value for the integral?
    • Homework 4.3
      • You've got to try those hard ones! Most everyone punted on #19 and #20.
      • You've got three free parameters: what degree do you think you can achieve?
      • Integrate an arbitrary quadratic, and match coefficients (the same idea we used last time to find the function g).
    • Homework 4.4
      • Midpoint is better than trapezoidal. It just doesn't look that way, because our authors do something frankly bad, and it even confuses them in their solutions manual.
      • Furthermore, and this is really bad, the algorithm doesn't work in the book.
        1. You can use midpoint for even and odd numbers of subintervals.
        2. You should use as many function evaluations as you have subintervals (e.g. n=4 means 4 function evaluations)
  • Section 5.1 homework due
  • There will be one more quiz, next Wednesday, over 5.2.

• Last word on Section 5.1
  • section 5.1 summary

  • #8a, p. 256
    • Try this!

• Section 5.2: Euler's method
  • section 5.2 summary (updated -- slight error at the end of my handout)

  • Problems from section 5.2:
    • 1a, 2a, p. 263