Day 32 in MAT229

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Announcements:
- Materials:
- We're in week 9, an this week we are talking about sequences and series.
- Note that we have a "spring break" day this week, so I'm going to issue two days of new notes only -- nothing on Friday. So Wednesday I'll drop some notes on series.
  Friday you should relax and have some fun.
- I've graded everything up to the lab you turned in on Saturday (IMath portion of the exam, which saw some dramatic changes to some of you; Weekly 5 assignment (key .nb, and .pdf); Lab 7 (key .nb, and pdf)).
  It definitely would have been helpful had you had the feedback from weekly assignment 5 and Lab 7 for the exam. That's my bad, so I'm going to only count exam 2 in your final grade if it benefits you.
  I may use your performance on it, however, to give some impression of how you are doing at midterm (those grades are due next week).
- I pushed back your homework due date on weekly homework 6 to tomorrow, Wednesday, because I can't get to it before then anyway....
- And now for something completely different: asymptotic (Thanks Shawn Huesman, for the recommendation! Here's another Shawn recommendation: Hello, World).
Today: Lab 9
1. Lab 9 concerns Taylor polynomials, and their remainders, and their use to approximate other, more complicated, functions.
  Yes, it's frequently about approximating complicated situations (functions) with simpler things.
  - Remember that computers do only four things very, very well:
    1. add
    2. subtract
    3. multiply
    4. divide
  - Polynomials only require those four operations, which makes them so wonderful for this job of approximation. We can build sines, exponentials, logs, etc. with polynomials -- functions that aren't computed with just those four arithmetic operations.
  - When we approximate, however, we're going to be making errors. So our focus today is on seeing the repurcussions; and learning how to choose the degree of the Taylor polynomial that will approximate the desired function to within a desired tolerance (error).
Materials for today:
1. Lab 9: Approximating functions with polynomials (.nb) (a pdf version)
Links/Notes:
- A reminder that we Zoom these labs. You're welcome to come virtually anytime.

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