Animations for a Lively Calculus

ICTCM 2001
Coreen Mett
Radford University

• goals
  • basic Maple tools
  • applications in calculus
• intro to Maple
  • restart
  • ?animate
  • table of favorite commands
  • publishing to WWW 
    • cycloid animation
    • animation in 3-D
  • lacking -- pixel generation, trace, zoom
• animation tools
  • animate command
  • naming plots (for display, overlay)
    • conic section (simple overlay)
    • cycloid (shifted overlay)
  • building frames --> display(...., insequence = true) command
• improvements
  • adding a tracking point (Inspired by Tilak de Alwis, ICTCM, November 1997)
  • adding text 
    • static
    • ticker (secant animation)
  • shading -- enhance a concept, but "expensive" (see area-convergence, area_build)
  • building in flexibility (Newton-zoom)
• applications in calculus
  • limit/convergence (illustrate area of region as limit of rectangles)
  • slope of tangent line as limit of slopes of secant lines
  • derivative-build (generate derivative function by calculating slope at each point)
  • epsilon-delta relationships in limit
  • Newton's method (flexibility -- try "start = 11" for f(x)=sin(x))
  • area-build
  • solids of revolution
    • animation
    • region between
    • region about ANY axes
  • conic sections
  • Taylor polynomial convergence
  • vectors in 3-D
  • cycloid generation
  • spirographs
  • parametric plots (parametric_movie.mws)