Some Applets for Math 131

You should see two buttons on this page, labeled "Riemann Sums" and "Slope Fields." (If you don't see any such buttons, then your Web browser does not support Java, and you can't use this page.) Clicking on one of these buttons will open a separate window where you can play with some Calculus II ideas.

Note that when you type a function definition into one of these windows, you must represent multiplication as "*" and exponentiation as "^". For example, "x times y squared" has to be written as "x*y^2".

Click on this button to open a new window you can experiment with Riemann Sums:

This applet can draws the area corresponding to a Riemann Sum for a given function f(x). It also computes the value of the Riemann Sum. You can select the Left Endpoint Rule, the Right Endpoint Rule, the Midpoint Rule, the Upper Sum [called "Circumscribed" in the applet], or the Lower Sum [called "Inscribed" in the applet]. The applet can also do the trapezoid rule (which is not strictly speaking a Riemann Sum).

Click on this button to open a new window where you can experiment with slope fields:

In this applet, you can enter dy/dx as a function of x and y. This is a simple first-order differential equation, which can be represented by a slope field. The applet shows the slope field. If you click on the slope field, the applet will solve the differential equation numerically and draw the solution curve. Numerical solutions are never completely accurate. In some cases -- near points where the value of dy/dx is undefined, for example -- the numerical solution is not even close. Three different solution methods are available. The most accurate, Runge-Kutta Order 4, is the default.