Where does the idea come from?

Dynamic Grapher is based on an idea from the Functions Group in the School of Education at the University of California, Berkeley, under Professor Alan Schoenfeld. The first versions were written at Berkeley in LISP in the early '90's. This version was written in Java by myself.

What does it let you do?

Dynamic Grapher is a function plotter. It allows you to enter and graph two dimensional functions in Cartesian, polar, and parametric coordinates. It also allows you to graphically solve first and second order differential equations and systems of first order differential equations.

Your functions can contain integrals, sums, and derivatives - good for calculus. Also, your functions can contain up to five parameters, which you can vary. The graph will change in real time as the parameter value changes.

Parameters and how to use them

The idea here is that you can enter in a function like y = a*x^2. (As of now you must have * for multiplication.) Dynamic Grapher will assume that the a has a value of 1 and will give you a slider to change the value of a up or down by a given increment. (The increment is 0.1 unless you change it.) As the a changes you will see the graph (a parabola) change with it in real time.

Your function can have any or all of the parameters a, b, c, n, and N. The N is special: it's value is always a non-negative integer, and it increases or decreases by 1 each time.

Try entering this into Dynamic Grapher: y = a*x + b. In the slider hold the mouse down on the right arrow. What happens?

Then do the same with the right arrow. Now click on the b button to select the b parameter. Play with the right and left arrows. What happens?

Integrals, sums, and derivatives

You can put integrals, sums and derivatives in you functions. Here are some illustrative examples:

y = int(x^2,0,x) is the function that is the integral of x^2 from 0 to x. Be sure to enter in the integrand in terms of x.

y = sum((-1)^n*x^(2*n)/(2*n)!, 0, 10) is the function that is the sum of (-1)^n*x^(2*n)/(2*n)! as the n varies from 0 to 10. The counter in the sum must be n. If you want you can replace the 10 by N and then make the N vary using the slider.

y = D(x^2,x) is the derivative of x^2. D(x^2,2) is the same derivative evaluated at x=2. The function that is differentiated must be in terms of x.

Functions that you name

You can name functions yourself, and then use the names in other functions. For example you can make y = x^2 into a function called f. To do this
  1. Click on New
  2. Click on y=f(x)
  3. Enter x^2, and click on Enable use in other functions
  4. Enter a single letter for the name of the function.
  5. Hit return or click on done.
  6. Click on Done

If you have created a function called f, then you can make any of these functions:

The applet

Click on the button to start the applet.