Introduction to Parametric Curves and Equations

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• Misc
  • Calculus Bee
    • April 23 (tomorrow), 4:00 - ?
    • Newton 203
• Questions?
  • Final will be cumulative but emphasizing material since 2nd exam
• Parametric Curves
  • Section 11.1
    • x = f(t), y = g(t) over interval I of t values from t=a to t=b
    • Points (x,y) = (f(t),g(t)) form parametric curve
    • Equations for x and y are parametric equations for curve
    • t is parameter, I is parameter interval
    • ( f(a),g(a) ) = initial point
    • ( f(b), g(b) = terminal point
    • Confusing examples...?
  • Examples
    • What do these generate?
      • x = sin t
      • y = 2 cos t
      • Ellipse
        
    • Spiral
      • Basic equations use sin and cos to circle, but increasing radius to make spiral
        • x = kt cos t
        • y = kt sin t
      • Implemented in R, and a figure it generates:
        

        spiral = function(  ) {
            k = 2.5
            t = seq( 0, 2*pi, length=100 )
            x = k * t * cos(t)
            y = k * t * sin(t)
            plot( x, y, type="l", col="red" )
        }

        
        
  • Problem set
• Next
  • Calculus and parametric equations
  • Read section 11.2 (“Calculus with Parametric Curves”)

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