# Flash and Math Applets

Flash applets on this page are authored by Barbara Kaskosz of URI and the Flash and Math team. If you are interested in the code behind the mathlets and developing your own applets, visit mathlets’ and tutorials’ home at Flash and Math.
Click, then right-click (Ctrl-click on a Mac) on the little surface to the right, to see what version of the Flash Player you have. For many applets below you need version 9 or higher. Click Download Flash Player to download the latest version of the player from the Adobe site. |

### Precalculus and Single Variable Calculus Applets

- Practice Sketching Derivatives 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. - 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.
- 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.

### 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.

### Statistics and Discrete Math Applets

- Interactive Histogram. This tool is used in many of the applets on this page. It illustrates the notion of “bin” that is important for understanding both histograms and distributions in general.
- Visualizing Sample Proportions. Simulates experimentally collecting sample proportions and creating a histogram to illustrate the theoretical mean and spread of the sample distribution.
- Visualizing Confidence Intervals for Proportions. Simulates experimentally collecting sample proportions and forming confidence intervals. The percentage of confidence intervals that contain the true population proportion is shown to illustrate the notion of “confidence level.”
- Visualizing a Sample Mean. Simulates experimentally collecting a single sample (from a population whose distribution is shown) and displaying summary statistics for that sample. Allows the user to repeat the experiment, collecting a set of sample means and even showing a histogram to illustrate the theoretical mean and spread of the sample distribution.
- Visualizing the Distribution of Sample Means. Simulates experimentally collecting sample means and creating a histogram to illustrate the theoretical mean and spread of the sample distribution. The theoretical distribution of the population is provided for comparison.
- Visualizing Confidence Intervals for Means. Simulates experimentally collecting sample means and forming confidence intervals. The percentage of confidence intervals that contain the true population mean is shown to illustrate the notion of “confidence level.”
- 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

- Mandelbrot Plotter – Generate and Export Beautiful Fractal Images in Flash We present a major Flash project for your enjoyment! This Flash-based Mandelbrot Plotter allows you to create and save beautiful fractal images. The application is full of zooming and coloring features which give you a great amount of control over your images. The images can be large and can be saved in JPEG or PNG formats.
- Graphing the Cantor Function Get insight into the graph of the Cantor function.
- Images of Math Curves – Create and Save In this effect, we use families of planar curves to create and save interesting images.
- 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.

### Awards for Flash and Math Applets

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

The FlashAndMath.com 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 Book

If you are interested in creating your own Flash applets don’t miss the 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. |

*Page last modified: August 17, 2012*