Introduction to Newton’s Method

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• Misc
  • Colloquium
    • “Perpetual Pest Control in the Face of Resistance Evolution?”
    • Dr. John Ringland, University of Buffalo
    • Thursday, Oct. 29, 4:00 PM
    • Newton 202
    • Usual extra credit
• Questions?
• Logical Operators
  • Section 13.3
    • Example logical variables a, b
      • a and b true (1) if a and b both true, otherwise false (0)
    • ~ is negation
    • Beware two operators on same line
      • a > b > c compares result of (a > b ) to c
      • Probably should have been (a > b) & (b > c)
    • Precedence
      • (...)
      • ~ (negates, not, turns true into false and vice versa)
      • & (and, true if both operands true)
      • | (or, true if either or both operands true)
  • Examples
    

    >> x = 17;
    >> y = -3;
    >> x > y
    ans =
         1
    >> (x < y) | (y < 0)
    ans =
         1
    >> p = 1;
    >> q = 0;
    >> p & q
    ans =
         0
    >> ~q
    ans =
         1
    >> 7 & 13
    ans =
         1

• Newton’s Method
  • Video
  • Example
    • f(x) = e^x - 10
    • Need f′(x) = e^x
    • Initial guess = 3
    • Tolerance helps detect completion as “small” changes in x
      
    • Tolerance = 10^-6 % = 10^-8
    • x₀ = 3
    • Rel. delta = 2e^-8
    • Iteration 1:
      • x₁ = x₀ - f(x₀)/f′(x₀) = 2.5
        
      • Rel. delta = 0.5/3 = 0.16
    • Iteration 2:
      • x₂ = x₁ - f(x₁)/f′(x₁)
      • … etc. …
  • Lab
    • Handout
• Next
  • Function handles and calculations on functions
  • Read sections 14.3 and 14.4

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