Math 5: Calculus Applets


 

 

 

 

Thanks to Professor Klotz for collecting these.

RIEMANN SUMS

  • This applet gives you the Riemann sum and the actual integral value. You can change what kind of sum you use and how many intervals, and change the shape of the graph by grabbing dragging.
  • This one lets you type in the function. Click "graph f(x)" to see the function, then click on the kind of sum you want.

OPTIMIZATION

  • Java applets illustrating the solution to finding the maximum area of a rectangle which can be inscribed in a semicircle.
  • Java applet illustrating the solution to finding the longest ladder which can be carried through a hallway with a corner.
  • Java applets illustrating the solution to finding the shortest time to move through the desert to a town.
  • Java applets illustrating the solution to finding the shortest ladder that can lean over a fence against a building.

NEWTON'S METHOD

  • Newton's method applet All the fun of Newton's method, without the tedious computations! (Doesn't seem to work with Netscape.)
  • Another Newton's method applet The slide bars at the bottom control the number of iterations and the intial guess. (Again, won't work on my Netscape.)

LIMITS

  • epsilon-delta applet You can read the instructions above the applet shown, then try it out. Then go down below it and hit the Launch EpsilonDelta button. That configuration of the applet has some examples in the pull-down menu that are well worth thinking about. NOTE: I haven't been able to get this one to work with Netscape. It's fine with IE, though.
  • generating tables to demonstrate limits Note that the instructions follow the applet and good examples follow them. NOTE: I haven't been able to get this one to work with Netscape either. It's fine with IE, though.
  • continuity applet This applet also allows you to experiment with the ingredients of the epsilon-delta definition of the limit.

DERIVATIVES

  • secant tangent applet Move the green dot toward the red one to see the secant line
    become the tangent. Pull down the menu above the graph for more provocative examples, or enter your own function, e.g. abs(x). Read the directions for how to zoom in, etc. NOTE: another one that won't work with my Netscape (4.77 for Mac).
  • function and derivative Move the slider to see the green slope change and to plot the derivative in red. Your goal is to obtain a visceral feel for what the slope is at a point (the value of the red function) and to relate the shape of the function to that of the derivative. Change functions and experiment. NOTE: one more Netscape failure
  • function, derivative, integral Click the Show Derivative box (ignore the integral for now; we'll get to it later). Then click and hold down on the graph, move it, and see the derivative change. To start again hit the browser Reload or Refresh button. NOTE: again, won't work on my Netscape.
  • derivative puzzles When you're comfortable with the being able to get the general shape of the derivative function from looking at the graph of the original function, play this derivative puzzle game that asks you to match function graphs with those of their derivatives.
  • surfing for derivatives A neat way to visualize the derivative.

Jim Wiseman

Department of Mathematics and Statistics
Swarthmore College
500 College Avenue
Swarthmore, PA 19081