Day 12 in Mat360

Today:

• Announcements
  • Alert! Quiz over Section 2.3 inexplicably lost! The hunt is on....

  • Return homework 1.3 -- Graded 4, 10, 16
    • This was a considerable disappointment.
    • Many people "gave up", or "never tried" several problems.
    • If you have questions on homework, ask in advance! I'm guessing that you're putting it off....
    • #4
      • we did an example like this one in class.
      • What results do you need to invoke?
    • #10
      • The first thing about algorithms: they're supposed to do what they advertise.
        • Did you handle all cases?
        • Did you try it out?
        • Did you try it in code? (Only one...)
        • Did you look at the student solutions manual? (n=1?)
      • Then they're supposed to do it well.
        • Don't do calculations twice. Define temporary variables.
        • Use the right formula!;) This was really the message of this exercise. What are we trying to avoid?
    • #16:
      • First, assume a limit exists.
      • Now: how do we know that a limit exists?

  • Problems for Newton's Method: 2; 4a; 5b,c; 7(b,c); 17; 18; 24; 33 (due Monday, 9/28)
  • NB: the reason I'm collecting Newton's method homeworks early (on a Monday) is so that I can get them back on Wednesday, in preparation for the exam on Friday.
  • Our first exam is Friday, 10/2 -- just FYI! It will cover through section 2.4, which we start next time. The homework for 2.4 may appear on the exam (rather than collecting it, I sometimes use this approach). So you want to be able to do the homework....
  • section 2.4 worksheet

• Section 2.3: Newton's Method
  • section 2.3 worksheet
  • section 2.3 summary

  • Remember: you should know the straightforward derivation of Newton's method, based on tangent lines.

  • #1, p. 62 (reprise)

  • A glimpse at its quadratic convergence (more of this in section 2.4)

  • A Mathematica notebook illustrating the relationship between the Newton iterates and the cobweb of the FP method.

  • The Secant method (and regula falsi):
    approximating the derivative with a finite approximation

  • Take a stab at drawing functions that will cause problems for each of Secant and Newton's methods.

  • Using Newton's method to make pretty pictures. Notice that there are also notebooks available which implement each of the methods on the Mathematica website. That's where I got the Regula Falsi notebook above.

  • Here's my version of that:
    (takes awhile!)