• Interactive Area and Arclength Approximations Using Flash
    The goal of this demo is to provide instructors and students with interactive tools for approximating area under a curve and arclength using elementary numerical methods. In put consists of a domain and function formula. Then the user selects points that need not be equispaced along a curve. (The points can be in any order.) The software then plots line segments for arclength approximation, forms trapezoids for the trapezoidal rule, or displays parabolic arcs for Simpson's rule and then provides a numeric approximation. These routines provide an opportunity to form estimates for functions which when used in integral expression have no closed form antiderivative. They also provide an opportunity to relate the geometry of the curve to adaptive numerical approximation. (This is a beta version of this demo. Please send comments. 7/14/2008.)
     

  • DEMOS for Related Rates
    In the gallery of related rate animations we have included three new demos:

    <> Filling a conical tank with a fluid. We simultaneously fill the inverted cone and show a corresponding triangle that simulates the change in height and radius of the cone of fluid.
    <> Searchlight rotates to follow a walker. We show a figure walking at a given rate and the beam of light following the figure. A triangle with changing hypotenuse is displayed along with a table of information.
    <> Filling a cylindrical tank, two ways. We compare filling a standard cylinder and the same cylinder laying on its side. As the fluid level rises we display a table of information about the volume, height of the fluid in each cylinder and the rate of change of the height in each cylinder. Graphs are also generated.
     

  • Matrix Algebra Demos
    Nine additional demos have been include in this collection, including inverse, linear combination, matrix transformations, span, closure and linear independence/dependence. Some of the demos now include a quiz or exercises to be done off-line. (8/25/2007)
     

  • DEMOS for MAX-MIN Problems
    In the gallery of many of the demos now have interactive Excel files for estimating the optimum value. These files can be downloaded for classroom use by instructor or for student experiments. (6/6/2007)
     

  • "Inverse" Box Problems
    This demo provides practice with word problems related to geometric figures. The sequence of "box problems" was designed to give students practice interpreting the given geometric characteristics of a box in order to determine the smallest rectangular piece of cardboard from which the box could be made. We present a sequence of geometric problems in which the object to be modeled is a box to be constructed in a particular way from a rectangular piece of material.  Since the dimensions of the box are specified we are not solving an optimization problem involving volume, rather we want to develop an algebraic model that can be used to determine the dimensions of smallest rectangular piece of cardboard that can be used to construct the particular box. Only algebra is required. Students must interpret geometric information given for the box in order to appropriately assign values to portions of the rectangle that circumscribes the unfolded box. (5/30/2007)
     

  • Box MaxMin Problems
    This demo provides practice with optimization problems related to geometric figures. A sequence of "box problems" is designed to help students develop an equation for the volume of a box constructed from a rectangular sheet of cardboard by cutting away portions and folding the remaining portions to construct a box in a particular way. The equation for the volume is to be formulated in terms of the dimensions L and W of the piece of cardboard and a parameter x, often related to the height of box, so that calculus can be used to determine the value of the parameter that will maximize the volume. An Excel file accompanies each type of box and provides a geometric model. The dimensions of the piece of cardboard can be changed and the volume of the largest box approximated. (5/30/2007) (This is a 'beta' version; please send us comments.)
     

  • Trip Stories
    This demo provides students with an opportunity to interpret graphical information from time vs. velocity graphs in order to create a story about an auto trip. Students should be familiar with the concept of the slope of a line segment so that the velocity of an object can interpreted. Included is an Excel worksheet with six auto trips represented by time vs. velocity graphs. The Excel worksheet is compatible with PC and MAC. In addition an animation in both Flash and QuickTime formats. (1/28/2007) 
     

  • Jogger: Time vs. Distance Graphs
    This demo provides students with an opportunity to use information on average rates of change to create a story about the workout of a jogger from a time vs. distance graph of the jogger's run. Students should be familiar with the concept of slope of a line, computing the slope of a line, and average rate of change. Included is an Excel worksheet with six jogger paths. The Excel worksheet is compatible with PC and MAC. In addition an animation with audio in both Flash and QuickTime formats. (1/11/2007) 
     

  • Sketch the Function from a Sketch of its Derivative
    This demo provides instructors with interactive examples for the classroom or student assignments that ask for a sketch of a function given a sketch of its derivative. Techniques for determining the type of sketch to generate, animations (using Flash and QuickTime), and 10 Excel routines which the derivative of a curve and simultaneously generate 3 possible sketches for the function are included. (1/2/2007)
     

  • Sketch the Derivative
    This demo provides instructors with interactive examples for the classroom or student assignments involving functions for which students are asked to sketch the derivative. Techniques for determining the type of sketch to generate, animations (using Flash and QuickTime), and 10 Excel routines which sketch a curve and simultaneously generate 3 possible sketches for the derivative are included. (12/29/2006)




Last updated 7/27/2008     DRH