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Animating Transformations
Rating

In most introductory linear algebra courses, prominent applications of transformations or mappings are moving (rotating, reflecting, translating), resizing (contracting, expanding), changing the shape (shearing, projecting) objects in the plane. A typical problem in such courses is to write the matrix of a transformation that changes points in such prescribed ways. The goal of this demo is to help students more easily visualize such transformations on a wide class of plane objects.

Subject:
Mathematics
Material Type:
Simulation
Provider:
Demos With Positive Impact
Provider Set:
Demos With Positive Impact
Author:
Hill, David R.
Roberts, Lila F.
Uebelacker, James
Whitley, Thurmon
Date Added:
01/24/2003
Applying Calculus to Approximate Volumes of Physical Objects
Rating

The purpose of this demo is to illustrate the use of the method of cross sections to find estimates of the volume of physical objects. The objects in this demo are not solids of revolution. The demo presented here utilizes Mathematica. Mathematica 5 notebooks are provided. The notebooks can be modified to approximate volumes of other objects for which a cross section approach is appropriate and a digital photograph is available.

Subject:
Mathematics
Material Type:
Simulation
Provider:
Demos With Positive Impact
Provider Set:
Demos With Positive Impact
Author:
Hill, David R.
Roberts, Lila F.
Date Added:
12/31/2003
Area Between Two Curves as Limits of Riemann Sums
Rating

This demo incorporates combines the visualization of approximating rectangles together with a graph of the approximate areas as a function of the number of rectangles. Thus, the limiting behavior of the approximating sums can be observed on the graph.

Subject:
Mathematics
Material Type:
Simulation
Provider:
Demos With Positive Impact
Provider Set:
Demos With Positive Impact
Author:
Hill, David R.
Roberts, Lila F.
Date Added:
05/13/2000
Area Estimates by Monte Carlo Simulation
Rating

This demo estimates the area of a circle or triangle using a probability experiment employing the Monte Carlo technique. We also indicate how to use our approach to estimate the area of a polygonal region.

Subject:
Mathematics
Material Type:
Simulation
Provider:
Demos With Positive Impact
Provider Set:
Demos With Positive Impact
Author:
Brenner,Regina
Hill, David R.
Roberts, Lila F.
Date Added:
06/02/2001
Area of Triangles and Other Regions
Rating

This demo illustrates two methods for computing the area of a triangle (and other regions) using the coordinates of the vertices. Both methods lead to interesting extensions which can provide topics for student investigation at a variety of academic levels.

Subject:
Mathematics
Material Type:
Simulation
Provider:
Demos With Positive Impact
Provider Set:
Demos With Positive Impact
Author:
Hill, David R.
Roberts, Lila F.
Date Added:
09/03/2002
Average Rate of Change
Rating

This demo provides students with a concrete understanding of the average rate of change for physical situations and for functions described in tabular or graphic form. Animations in gif and Quicktime format are available, as well as Excel programs for classroom or student use.

Subject:
Mathematics
Material Type:
Simulation
Provider:
Demos With Positive Impact
Provider Set:
Demos With Positive Impact
Author:
Hill, David R.
Roberts, Lila F.
Date Added:
04/21/2005
Bacteria Allocation
Rating

This demo develops a procedure for randomly allocating bacteria to a fixed number of droplets from a total of 100 droplets using a probability experiment employing the Monte Carlo technique.

Subject:
Mathematics
Material Type:
Simulation
Provider:
Demos With Positive Impact
Provider Set:
Demos With Positive Impact
Author:
Haigh, W.E.
Hill, David R.
Roberts, Lila F.
Date Added:
05/24/2001
A COLORFUL Linear Combination Demo
Rating

THis demo provides an application of linear combinations to construct colors displayed on computer screens. This colorful demo provides a realistic example of linear combinations in action. BOth MATLAB and Java routines are included.

Subject:
Mathematics
Material Type:
Simulation
Provider:
Demos With Positive Impact
Provider Set:
Demos With Positive Impact
Author:
Hill, David R.
Roberts, Lila F.
Date Added:
05/07/2001
A Carpenter Draws an Ellipse
Rating

This demo illustrates how a carpenter can draw an ellipse on wood or a sheet of wall board using simple tools. A "jig" can be used to demonstrate the technique and there are software animations to illustrate the use of the "jig".

Subject:
Mathematics
Material Type:
Simulation
Provider:
Demos With Positive Impact
Provider Set:
Demos With Positive Impact
Author:
Comfort, Sean
Hill, David R.
Roberts, Lila F.
Date Added:
03/26/2004
Cell Phones: Signal-to-Interference Ratio.
Rating

This demo develops a function that measures the power of the signal of a cell phone as a user moves in a cellular network and then determine the position in the network when the signal is a maximum.

Subject:
Mathematics
Material Type:
Simulation
Provider:
Demos With Positive Impact
Provider Set:
Demos With Positive Impact
Author:
Hill, David R.
Roberts, Lila F.
Date Added:
12/29/2004
A Collection of Elementary Probability Demos
Rating

This demo collection approaches probability through demos and experiments by using simulations via the Monte Carlo method. The collection includes interactive experiments for estimating the area of a circle, simulation of a network, allocation problems, creation of a rainbow, and choosing segments & drawing circles within a circle.

Subject:
Mathematics
Material Type:
Simulation
Provider:
Demos With Positive Impact
Provider Set:
Demos With Positive Impact
Author:
Brenner,Regina
Haigh, W.E.
Hill, David R.
Roberts, Lila F.
Date Added:
10/31/2014