• Derivative of vector-valued function
  • Tangent vector as a limit (Quicktime format)
    Animation to illustrate the limiting process involved in the definition of the derivative: control h using the slider
  • The tangent vector at the point
    The derivative gives a tangent vector
  • Tangent vectors from the derivative
    The derivative of the elliptical helix as another vector-valued function.
• Arc length
  • Arc length animation (BIGGGG...)
    Approximating arc length on a helix-like curve
  • Arc length animation (Quicktime format)
    Same animation as above with control of delta t using the slider
  • Derivative of a curve that sweeps out a trefoil knot
    Animation to illustrate the speed at which a point traverses a curve