Day 05 in Mat360

Today:

• Discuss (and ultimately collect) problems, 1.1.

• Questions/Comments on old stuff?
  • Email from a student re homework 1.1
  • It turns out that the maximum of the third derivative is at the endpoint anyway (which you could demonstrate by considering the sign of the derivative, for example). Nathan's bound on f''' (1.5*exp(.5)) was just a little larger than necessary (too "conservative"):
  • Maclaurin series for arctan via l'Hopital's rule
  • Maclaurin series for arctan via complex numbers
  • My method, using power series differentiation

• Section 1.2:
  • section 1.2 summary

  • (but can't fix the errors in the textbook!;)
  • Problems from section 1.2:
    • Let's look at some homework problems, if there's time....