David Little  
Mathematics Department Penn State University Eberly College of Science University Park, PA 16802 
Office: 403 McAllister Phone: (814) 8653329 Fax: (814) 8653735 email:dlittle@psu.edu 



Antiderivatives and Slope Fields
The following applet can be used to draw slope fields for the differential equation y' = f(x). Simply enter the function f(x) and the values a and b. The applet automatically draws a sample solution (in red) through the point (a,b). The applet also draws the graph of the function y=F(x) in gray. If F(x) is an antiderivative of f(x), then each blue line segment that passes through the same point as the graph of y=F(x) will also be tangent to the curve y=F(x). Furthermore, if y=F(x) is an antiderivative of f(x) and goes through the point (a,b), then the sample solution and the curve y=F(x) should match exactly. The values a and b can be changed by simply typing a new value, such as "1.2345", "pi/2", "sqrt(5)+cos(3)", etc. You may also change these values by using the up/down arrow keys or dragging the corresponding point. To move the center of the graph, simply drag any point to a new location. To label the xaxis in radians (i.e. multiples of pi), click on the graph and press "controlr". To switch back, simply press "controlr" again. Here is a list of functions that can be used with this applet.
© 2007 David P. Little Download this applet for offline viewing (includes source code). The above applet uses the Java Math Expression Parser (JEP) developed by Singular Systems 