Day 08 in Mat360

Today:

• Announcements:
  • Accounts are available for all in the Lab. Use your NKU username and password.
  • Any (repaired) versions of 2, 12, 24?
  • Homework 1.2 due today
  • Handout for section 2.2: fixed point iteration
    • worksheet

• Let's wrap up section 1.3:
  • Convergence:

    Convergence basically means that you're getting close to something, and we're interested in characterizing the rate at which we're closing in. Let's look at a few examples. One thing that you'll notice is the utility of the Taylor series here.

    • 6c, p. 37
      If there exists a positive constant such that

      

      for large values of n

      then we say that converges to with rate of convergence .

    • 7d, p. 37
      Suppose that

      and

      .

      If such that

      

      for sufficiently small h, then .

• Section 2.1:
  • section 2.1 summary

  • section 2.1 worksheet

  • You might try the java algorithms that are on-line
    • What's wrong with this program?

  • Consider the Mathematica file (warning! These are very primitive....)
    • Same problem....

  • Problems from section 2.1:
    • #3b
    • #8a