Introduction to Numeric Integration

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• Misc
  • Grade-by date for Newton lab is now Thursday, Nov. 5
  • A spring computing course
    • Math 304, Theory of Computability
    • What can you compute?
    • Needs Math 239 as prerequisite
    • MWF 9:30 - 10:20
  • Colloquium
    • “The Single Distance Problem”
    • Dr. Michael Bennett (Geneseo math alum, Ph. D f/ UR(?), now at RIT)
    • Wednesday, Nov. 4, 2:45, Newton 204
    • Extra credit as usual
• Questions?
• Numerical Integration
  • Video summary
    • Find area under curve aka find definite integral
    • Riemann using rectangles
    • Width of rectangle = delta x = x_i+1 - x_i
    • More rectangles give better approximation to area under curve
    • Left Riemann sums
      • Evaluate function at x_i
      • Delta x = (b-a)/n, n = number of desired rectangles
      • Summation notation
        
    • Trapezoid rule
      • Area = 1/2 delta x ( f(x₀) + 2f(x₁) + … + f(x_n) )
  • Example
    • Why?
      • Example helps you understand problem
      • Thinking about how you solve the problem by hand can suggest an algorithm for it
      • Solved example(s) become test case(s) for a program when you write one
    • Integrate f(x) = x² from x = 1 to 5 with 4 intervals
      
  • Lab handout
• Next
  • The for loop
  • Read sections 12.5 through 12.7

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