Department of Mathematics 5 Lippitt Road
Kingston, RI 02881
p. 401.874.2709
f. 401.874.4454
Lippitt Hall, room 200
mathdept@math.uri.edu
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.
Matching Formulas to Data
Plot points,
enter any parametric family of functions, dynamically change parameters while observing the
changes in the least square error.
Sequences
and Series of Functions Explore sequences and series of functions.
Plot Taylor and
Fourier polynomials. Examine pointwise and uniform convergence.
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.
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.
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.