Examples of Vector-Valued Functions

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• Misc
  • Times when MLC has tutors experienced in this course
    • Mon: 1 - 3:30, 7 - 10
    • Tues : 10:30 - 3:30, 7 - 10
    • Wed: 1:30 - 3:30, 7 - 10
    • Thurs: 10:30 - 3:30, 7 - 10
    • Fri: 1 - 2:30
• Questions?
• Vector-Valued Function Examples
  • Recall the Animated Snake
  • Function to generate “spine” of snake (without vertical neck)
    
    • r(t) = ⟨ t, sin t, 0 ⟩
    • Plotted in muPad:
      
    • How do you fill out a body around this curve?
      
    • Calculate T
      
  • Add a neck
    • snake(t) is a piecewise function
      • body = ⟨ t, sint, 0 ⟩, 0 ≤ t ≤ 6π
      • neck = ⟨ t, 0, e^t-6π-1 ⟩, 6π < t ≤ 6π+1
    • muPad version:
      
    • Is this continuous?
      • Yes, because limits of body and neck as t approaches 6π are equal, visually there is no gap
      • But its derivative is not continuous, seen as sharp corner where body and neck meet
• Next
  • Integrating vector-valued functions
  • Read section 13.2

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