Day 19 in MAT229

• Finishing off Week 5: This week we're featuring another analytic integration technique (trig substitution), and numerical integration (when all else fails).

• A snow delay! Geez, what does the weather have against our labs? First a cancellation, then a delay. I ran the lab virtually yesterday, and you can check out our lab day page for the week to get a recording if you missed it, and for details of the lab.

• You do have a Weekly assignment #4. It is due Wednesday, after we return from "break".

• We have a break next week, with Monday and Tuesday off. So I won't be putting out new material, or hosting office hours. You can still reach me, however, by email; let me know if you are struggling with anything.

  Enjoy your break!

We started numerical integration last time, with a focus on the schemes. Today we focus on a review of the methods, and more focus on the error term -- looking at some specific examples, and, in particular, how to use the number of sub-interals $n$ to get the accuracy we desire in an approximation.

Today I lead you through the Mathematica file, reviewing the rectangle methods, showing you where to find some little routines for doing these approximation schemes (trapezoidal, midpoint, and Simpson's rules), and looking at the errors the schemes make.

1. Numerical Integration (pdf)
2. Numerical Integration (nb)
3. Long's high points of Numerical Integration (part I -- last time)
4. Long's high points of Numerical Integration (part II -- review and errors)

• 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.
• Numerical Integration on-line.