First Year Calculus

• Graphs and growth rates as functions of a parameter.
• Study failure modes of Newton's method graphically and numerically.
• Reason using calculus ideas from numerical data.
• Study Riemann sums as functions of mesh size.
• Behavior of Monte-Carlo methods of integration.
• Compare Taylor polynomial graphs and values to original functions.
• 1-D differential equations (e.g. ones without closed form solutions) graphically.
• Experimentation to support infinite sequence and series intuition. (Including the limitations.)
• Web Resources:

  Mathlab:

  http://www.mathlab.cornell.edu/computer_and_portfolio/index.html#ONEVAR

  Visual CalculusModules:

  http://archives.math.utk.edu/visual.calculus

  Calculus on the Net:

  http://www.calculus.net

  Rose-Hulman Calculus Problems:

  http://www.rose-hulman.edu/Class/CalculusProbs

  Famous Curves Applets:

  http://www-groups.dcs.st-and.ac.uk/ history/Java/index.html

  Function Grapher:

  http://people.hofstra.edu/staff/steven_r_costenoble/Graf/Graf.html

  Family Plotter:

  http://www.shu.edu/projects/reals/classes/PlotFamily.html