Introduction to Green’s Theorem

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• Misc
  • SOFIs
    • Helpful to me in teaching this (or other) courses in future
    • Access through myGeneseo/KnightWeb
  • Final
    • Dec. 17 (Thursday), 8:00 AM, usual classroom
    • Comprehensive but emphasizing material since 2nd hour exam (e.g., multiple integrals, line integrals, vector fields, conservative vector fields, Green’s Theorem, etc.)
    • Rules and format similar to hour exams, especially open references
    • Except designed for 2 hours, you have 3+
    • Donuts and cider
• Questions?
  • Problem set question re constant magnitude radial force?
    • Think of √(a² + f(a)²) as distances
    • Constant magnitude radial force is conservative, work doesn’t depend on path
      
  • Question 4 (is ⟨x²,y²⟩ gradient field)?
    • Connection to problem 3?
    • Field in problem 3 = ⟨x²,y²⟩
    • Gradient field → conservative → circulation around closed curve = 0
    • Circulation & flux integrals around closed curve?
      
• Non-Conservative Vector Field Example
  • F(x,y,z) = ⟨ 1, yz, z² ⟩ isn’t conservative, but we wanted to see what happened if we tried to find a potential function for it anyhow.
    
• Green’s Theorem
  • Summary of section 16.4
    • Something re F(x,y) = ⟨ M(x,y), N(x,y) ⟩…
    • Two forms
      
• Next
  • Green’s Theorem examples

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