In this part of Flash & Math you will find a large and growing collection of self-contained learning and teaching modules for mathematics - math appplets, i.e. mathlets. Mathlets can be used by instructors for classroom demonstration, and by students for self-paced study and exploration. They are all programmed in ActionScript and run in the Flash Player. If you are interested in developing you own mathlets, visit the second part of our site: ActionScript 3 Tutorials for Flash Developers. Come back to our site often for new mathlets!

## A FEW SAMPLE MATHLETS

New: Slope Field Applet The applet plots the slope field for any ordinary differential equation of the form dy/dx=f(x,y) entered by the user. The user controls the x and y ranges as well. Approximate solutions based on the slope field can be drawn with the mouse.

New:
Practice Sketching Derivative
The applet illuminates the relationship between graphs
of functions and their derivatives. A graph of
a randomly generated function *f(x)* is provided. The student attempts to sketch the graph
of the derivative *f '(x)* by dragging and shaping a curve. The answer is evaluated for correctness
at a click of a button providing instant feedback.

Contour Diagram Plotter and 3D Function Grapher Applets Combined This applet combines a contour diagram plotter and a 3D function grapher, and allows the user to toggle between the two. Since both contour maps and 3D graphs are very sensitive to the choice of x and y ranges, it is often very hard to interpret a contour diagram without seeing the corresponding 3D graph. This applet gives an opportunity to compare these two ways to visualize functions of two variables.

Implicit Equations Grapher
This applet graphs user-defined implicit equations of the form
f(x,y)=g(x,y) in a user-defined x,y ranges. The syntax used for input
is the same as graphing calculator syntax and the applet is very easy to use.
The results are comparable with those provided by CAS like *Maple*.

Matching Formulas to Data Plot points, enter any parametric family of functions, dynamically change parameters while observing the changes in the least square error. Quick and easy matching formulas to data points.

Parametric Curves on the Plane Graph paramertic curves in rectangular as well as polar coordinates. Curves can be traced showing the direction of motion and the way a curve is traversed. The x and y ranges adjust automatically.

Derivative Plotter Enter a formula for an arbitrary function, the applet will plot it. Try sketching the derivative by drawing on screen. Reveal the real derivative dynamically by dragging a slider while the lineal element corresponding to the tanget line and its slope are displayed.

Sequences and Series of Functions Plotter Enter a formula for a sequence or a series of functions, the applet will plot consecutive terms or partial sums at a click of a button. In particular, you can enter Taylor series or Fourier series. You can also enter a piecewise defined limit function to be plotted. Many demo examples are provided.

3D Function Graphers Enter a formula for f(x,y) in terms of x and y, the ranges for x and y, and the graphers display the graph of the function of two variables f(x,y) in 3D. You can rotate the graph in real time and change its transparency to see the surface clearly.

Parametric Surfaces in Rectangular Coordinates Enter parametric formulas for the x, y, and z coordinates, and the grapher will display the corresponding surface in 3D. You can rotate the graph in real time and change its transparency for better understanding of the surface.

Spherical Coordinates Presented Interactively Move a point in 3D and see its spherical coordinates change. Many multiple choice practice problems will help you gain an insight into spherical coordinates. Especially that pesky phi coordinate!

Double Integrals in Rectangular and Polar Coordinates Enter the limits of integration in double integrals and see the planar region that they describe. Practice finding limits in Cartesian and in polar coordinates that correspond to a given region on the plane.