Day 04 in Mat360

Today:

• Wrapping up Section 1.1:
  • Proof of Taylor's Theorem (finished)
    • Last time we looked at the induction piece.
    • the error term is derived using the Weighted Mean Value Theorem for Integrals.

  • Problems from section 1.1:
    • You want to find software that will allow you to reproduce the Maple work presented in the text (and learn how to do most things on your calculator, of course):
      
    • Taylor Series:
      • It's nice to be able to check and see that you're getting appropriate values.

    • Which others problems, perhaps from homework, would you like to look at?

• Questions/Comments on old stuff?
  • Don't forget to use your calculator and/or software!
  • Our tests will be in two parts: half in class, half out of class (using whatever software you like).

• Section 1.2:
  • New assignment on the assignment page

  • Quiz 2

  • Okay: we know that we're going to make errors
    • Approximating functions with polynomials.
    • All reals are rational, to a computer.

  • So, questions:
    • How do we avoid or prepare for errors?
    • How do we measure errors?
    • How do we minimize errors (since we're guaranteed to get some)?

  • section 1.2 summary

  • section 1.2 worksheet

  • Problems from section 1.2:
    • 1b
    • 2b
    • 3b
    • 4d
    • 13b
    • 17