Vector Fields

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• Misc
  • REU Talk
    • Megan Brunner
    • Measuring intercultural competence in middle school students
    • Thursday, April 14, 3:30, South 328
    • Extra credit for write-ups
• Questions?
• Integration Problem Set
  • Handout
• Vector Fields
  • First 2 parts of section 16.2
    • Vector fields describe, e.g., moving fluid in region
    • Function that assigns vectors to points?
      • We’ve seen functions that assign vectors to individual numbers, e.g., f(t) = ⟨ 8t, sin t, t² ⟩
      • And functions that assign numbers to points in space, e.g., f(x,y,z) = xy + sin z
      • Vector fields combine these ideas, e.g., f(x,y,z) = ⟨ xy, sin z + x², xyz ⟩
    • Sketch fields with tails of arrows at points vectors go with
    • Gradient field gives vector pointing in direction of greatest increase, magnitude is directional derivative — gradient formula
  • Examples
    • Electric field in a simple vacuum tube
    • Also a vector field with all vectors parallel
      
    • Plotting vector fields with muPad
      
    • Gradient field of F(x,y,z) = x² + xy - z
      • ⟨ 2x+y, x, -1 ⟩
        
• Next
  • Line integrals of vector fields
  • Read “Line Integrals of Vector Fields” and “Line Integrals with Respect to dx, dy, or dz” parts of section 16.2
    • Last 1/3 page 947 through bottom of 949

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