David Little
Mathematics Department
Penn State University
Eberly College of Science
University Park, PA 16802
Office: 403 McAllister
Phone: (814) 865-3329
Fax: (814) 865-3735
e-mail: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 x-axis in radians (i.e. multiples of pi), click on the graph and press "control-r". To switch back, simply press "control-r" again.

Here is a list of functions that can be used with this applet.