Day 18 in Mat360

Today:

• Announcements:
  • Courtney had bad luck with that Muller's method, but she was close!

    Your homework is graded. You got most of the points for effort! Please attempt the homework (and use Mathematica!).

  • Speaking of which, your first project is due 3/21.

• Today I want to emphasize Taylor's theorem, as we look at a couple of different problems. Taylor's theorem is at the heart of almost everything we do from now on. You need to understand it well!
  • A comment on "Big-Oh notation", in relation to Taylor's Theorem 5.1, p. 172

  • An important example: order of convergence the Secant Method (Theorem 3.5, p. 99)

    Even though the order of convergence is less, the routine may run in about the same time as Newton's (depends on the problem, of course).

  • The "linear spline" error term (section 5.5)

  • The general polynomial interpolator error term (Theorem 5.3, p. 193)

• Notes from Class:
  • Polynomial Interpolation schemes
  • Proof of Order of Convergence of the Secant Method