Flash mathlets -- mathematics applets -- on this page are authored by Barbara Kaskosz of the University of Rhode Island, many jointly with Doug Ensley of Shippensburg University. If you are interested in the code behind the mathlets and developing your own applets, visit mathlets' and tutorials' new home at Flash and Math. Consider also the Flash and Math Applets book described below.

The book presented here, the Flash and Math and MathDL Flash Forum websites, as well as many of the applets below were created during a joint project by Barbara Kaskosz and Doug Ensley. The project that began in 2005 was sponsored by the National Science Foundation and the Mathematical Association of America. The project focused on creating materials and providing training for math and science educators interested in authoring online learning materials using Adobe Flash.

Recently, the FlashandMath project was honored by the International Conference on Technology in Collegiate Mathematics (ICTCM) with the 2009 ICTCM Award for Excellence and Innovation with the Use of Technology in Collegiate Mathematics.

Flash and Math Applets Book If you are interested in creating your own Flash applets don't miss the new book: 'Flash and Math Applets: Learn by Example' by Douglas Ensley and Barbara Kaskosz. The book will teach you from scratch and step-by-step all you need to know about Flash to create applets like the ones above. Peek inside and download sample chapters from flashandmath.com. Buy from amazon.com.

The book teaches how to use Flash and ActionScript 3 programming by examples, many of which are based on the popular tutorials at flashandmath.com:

The collection of Flash mathlets presented on this page has just been awarded the MERLOT Award for Exemplary Online Learning Resources - MERLOT Classics 2009 by Multimedia Educational Resource for Learning and Online Teaching (MERLOT).

APPLETS

Multivariable Calculus Applets

• 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.
• Surfaces in Rectangular Coordinates   The user enters parametric equations for rectangular coordinates, the applet draws a surface that can be rotated in real time.
• Parametric Surfaces in Cylindrical Coordinates  The user enters parametric equations for cylindrical coordinates.
• Parametric Surfaces in Spherical Coordinates  The user enters parametric equations for spherical coordinates.
• 3D Function Grapher  The user enters a formula for f(x,y) and the x and z ranges.
• Motion in 3D The user enters parametric equations for an arbitrary curve in xyz-space. The curve can be traced while the velocity and the acceleration vectors are displayed as well as their approximate values.
• Regions Described by Double Integrals  Enter limits in double integrals in rectangular and polar coordinates to see the region described by those limits. Practice finding limits which describe a given region.
• Spherical Coordinates  Become familiar with spherical coordinates. Enjoy many practice problems.
• Parametric Curves in 3D  Plot parametric curves in the xyz-space. Enjoy many examples and practice problems.

Precalculus and Single Variable Calculus Applets

• 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. Of interest in a Multivariable Calculus course as well.
• The Definite Integral in Terms of Areas  A simple applet that dynamically illustrates the interpretation of the definite integral in terms of areas.
• Matching Formulas to Data  Plot points, enter any parametric family of functions, dynamically change parameters while observing the changes in the least square error.
• Parametric Curves on the Plane  Plot curves in rectangular as well as polar coordinates.
• Sequences and Series Plotter  Plot sequences of numbers. Explore convergence of sequences and series.
• Sequences and Series of Functions  Explore sequences and series of functions. Plot Taylor and Fourier polynomials. Examine pointwise and uniform convergence.
• Accumulated Change and Antiderivative Plotter  Plot accumulated change given a rate of change; see the Fundamental Theorem in action; plot antiderivatives.
• Derivative Plotter  Practice plotting derivatives. Have the applet graph the derivative of any function you want.
• Families and Points Plotter  Plot points, match formulas to data. Explore families of functions.
• Functions Grapher  Graph functions. Trace their graphs. Find points of intersection.

Discrete Math Applets

• Truth Tables  This series of applications addresses basic formation of tables, logical equivalence of propositions, and applications to everyday arguments.
• Graph Theory   Explore the basic definitions of Eulerian, Hamiltonian, planar and isomorphic.

Other Applets

• Graphing the Cantor Function  Get insight into the graph of the Cantor function.
• The Beauty of Parametric Curves  Create spectacular graphics while learning about parametric curves.
• The Game of Marienbad  Take a break with a friendly game of Nim.