Divergence and Curl

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• Misc
  • Extended Math Learning Center hours for finals
    • Opening 9:30 (instead of 10:30) AM weekdays
    • 7:00 - 10:00 PM Sunday, May 8
  • Final
    • Monday, May 9, 12:00 noon
    • In our classroom
    • Comprehensive, but emphasizing material since 2nd hour exam (e.g., multiple integrals, line integrals, Green’s theorem, applications, etc.)
    • Designed for 2 hours, you’ll have 3+
    • Rules and format otherwise similar to hour exams
    • Donuts and cider
  • SOFIs
    • Helpful to me in planning future offerings of this course
      
    • Thank you to those who have filled them out
    • Still a day and a half for those who haven’t
• Questions?
• Divergence and Curl
  • “Divergence in Three Dimensions” and “The Curl Vector Field”
    • Formulas
      
    • Physical interpretations
      • Divergence: positive implies expansion, negative contraction
      • Curl: ???
      • Measures of portions of a vector field that point out of a small circle around a point as opposed to circling around that circle
        
  • Example: find ∇⋅F and ∇×F for F(x,y,z) = ⟨ x²yz, xy²z, xyz² ⟩
    
  • Properties of divergence and curl
    • ∇⋅(∇×F) = …?
      
    • ∇×(∇f) = …?
      
      • Since gradient fields are always conservative and vice versa, this is where the component test for conservative fields comes from
• Questions from Anywhere in Course?
  • Finding bounds for triple integrals, e.g., section 15.5 exercise 5?
    

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