Day 02 in Mat122

Today:

• Roll

• Homework/directed reading handout: Section 4.7 (html) (pdf)
• Homework/directed reading handout: Section 5.1 (html) (pdf)

• Section 4.7: Newton's Method
  • Some: #2, p. 235
  • others: f(x)=1/x-7

• Section 5.1:
  • Dirt!
    • Suppose that you clock your speed at each minute along a trip, in mph:

      minute	0	1	2	3	4	5	6	7	8	9	10
      speed (mph)	0	30	45	30	70	65	70	70	45	30	35

      Estimate the distance travelled.

  • Trapezoidal rule
    • Assumes continuity of underlying speed function
    • We fit straight line segments between data points

  • Left/Right/Midpoint rules
    • relax continuity! Use rectangles...
    • also called rectangle rules: lrr, rrr

  • Basically, every function can be used to create a table like this, and then we can use these strategies.

  • Here's an important theorem:

  • Examples:
    • #5, p. 258 (also trapezoidal)
    • #9, p. 258