- Your 11.6 homework is returned:
- 26
- 30
- 40
- Your 11.7 homework homework is returned:
- 6
- 24
- 33
- You have an exam in exactly one week, next Tuesday. It will cover
11.2 through 11.9. So the material that we're working on today, Taylor
series, and the little dab we do from chapter 12 will appear on the
final.
Speaking of the "little dab": the material in chapter 12 is especially useful to computer science folk. So the three days we devote to it after Thanksgiving are especially important for you. Not that it isn't important for others! I'll be compiling a greatest hits.
On another important note: I won't be here for two of those three days. I expect that Steve Wilkinson will be leading you through that material. He's a great one to do so -- it's a favorite topic of his.
- How is your worksheet coming? Remember that some problems from the
worksheet will appear on both of your next two tests.
- Policy shift: your final exam grade will be used to replace your lowest test score. So there is an advantage to kicking in the final turn of this race!
- The big picture: we're approximating functions (some nasty) with nice ones (polynomials):
Let's talk error now. Remember error? As we discussed for the case of Simpson's rule, it's nice to give an estimate -- but even nicer when you can provide an error estimate, also....
- Examples:
- Let's find the Taylor series for ln (which is one that Nick asked about) around 3. That is, we're looking for values of
for arguments of around
. We can do it in two different ways:
- using our favorite geometric series, and
; or
- using Taylor polynomials, and
.
- using our favorite geometric series, and
- Taylor Polynomials Lab (from Stewart's Calculus)
- Let's find the Taylor series for ln (which is one that Nick asked about) around 3. That is, we're looking for values of
