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| Index of Interactive Materials For Classroom Demonstrations | ||
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The Unit Circle This applet can be used to introduce the idea of the unit circle. A slider allows the user to change the central angle, showing the corresponding coordinates along the circle. The radius of the circle can also be changed to emphasize sine and cosine ratio definitions. Relevant Courses: Math III, Precalculus |
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The Sine Function This applet shows the typical sine function being generated as a point rotates around a circle. This is a nice demonstration to emphasize the periodic nature of the trigonometric functions as well as the general properties of sinusoidal functions. Relevant Courses: Math III, Precalculus |
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The Trigonometric Functions The trigonometric function applet gives a dynamic graphical representation of all six trigonometric functions defined using the unit circle. The main idea is to to justify the name for each of the six trigonometric ratios. Relevant Courses: Math III, Precalculus |
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Function Transformations This was the very first applet, and the one that inspired this whole site. A series of sliders are used to vary parameters upon which a function is defined. The function can be changed in order to explore properties of function transformations. Relevant Courses: Math I, Math II, Math III, Precalculus, Calculus |
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Function Operations This applet allows the user to define a function based on two previously defined functions. In this way a function can be defined as the composition of two other functions, for instance. All functions and their corresponding relationships can be defined by the user. Relevant Courses: Math III, Precalculus, Calculus |
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Secant-Tangent Lines The typical secant line that slowly begins to look like the tangent line to a function at a given point. This dynamic demonstration will allow for the visualization of the "average rate of change" of a function and the "instantaneous" change. Relevant Courses: Precalculus, Calculus |
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A Function And Its Derivative A function is defined. As a slider moves, the tangent line is drawn on the function at all points on its domain. The user has the option to see the derivative of the function being drawn. By hiding the original function, the user can explore the ideas of antiderivatives. Relevant Courses: Calculus |
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Symmetry This applet can be used to study function reflections. Reflections about the x-axis, y-axis, origin and the line y = x are all possible. The function can of course be changed in order to customize the applet to the desired situation. Relevant Courses: Math III, Precalculus, Calculus |
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Polar Equations The Polar Equations applet allows the user to enter an equation of the form r = r (theta). The plotting is done by changing the values of the angle by means of a slider. Another slider permits the shading of specific regions on the plot. Relevant Courses: Precalculus, Calculus |
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Parametric Equations Equations of the form x = x (t) and y = y (t) are plotted for specific values of the parameter t. A slider changes the parameter values and allows the step by step plotting of the corresponding equation. Relevant Courses: Precalculus, Calculus |
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Vector Addition This applet defines two vectors u and v that can be changed in any way. It then gives a graphical representation of the sum of the two vectors, w = a u + b v. Vector addition and subtraction can be easily explored by changing sliders. Relevant Courses: Precalculus, Linear Algebra |
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Taylor Approximations The expansions can be about any point on the domain of the function, which the user has the ability to modify. The degree of the polynomial can be varied by means of another slider, ranging from 0 to 25. The polynomial expansion can also be shown on the screen. Relevant Courses: Calculus |
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The Least Squares Line Points can be entered with a click of the mouse or by entering its coordinates. The best fit line is then shown, with its corresponding equation and correlation. Entered points can be moved to explore many interesting characteristics. Relevant Courses: Math III, Precalculus, Calculus, Statistics |
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The Median-Median Line Points are entered with the mouse or by typing their coordinates. A series of buttons guides the user in a step by step construction of the median-median line. All elements of the construction can be set to "hidden" to show just the final approximation line. Relevant Courses: Math III, Precalculus, Statistics |
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The Normal Distribution C\The user can change the standard deviation and the center of the distribution to see an approximate value of the area under the curve, as a slider scans the bell curve. Relevant Courses: Math III, Statistics |
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A Monte Carlo Simulation A typical bull's eye simulation. Darts are thrown randomly inside a square region. Those darts landing inside the inscribed circle are counted as "hits". The user can throw as many as 5000 darts at once. Nice simulation to approximate Pi. Relevant Courses: Math III, Statistics |
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The
Triangle Inequality This applet allows the user to divide a stick into three parts. What conditions need to be met in order to be able to build a triangle with the three pieces cut? This gives students an intuitive representation of the problem. Relevant Courses: Math II, Math III, Precalculus, Calculus |
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The
Hypercube Projections Idea taken from our text Linear Algebra through Geometry by Thomas Banchoff. Sliders in this applet allow for the explorations and rotations of the hypercube. Relevant Courses: Linear Algebra |
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Generic Applet (All Purpose) This is simply a generic GeoGebra applet application. This is the program used to build all applets in this resource. It is intended for teachers and students to get an initial "taste" of the capabilities and power of GeoGebra. Many features... Relevant Courses: All courses |
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Slope Fields Applet This GeoGebra application draws the slope field corresponding to a given differential equation. The user can also plot specific solutions by entering the point on which such solution should pass. Beautiful Dynamic behavior! Relevant Courses: Calculus |
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Riemann Approximations This GeoGebra application draws the rectangles representing left sums, right sums, midpoint rule and trapezoidal rule. It also draws lower and upper sums and calculates the corresponding approximations. Many features can be changed to satisfy all needs. Relevant Courses: Calculus |
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Figures Of Lissajous Idea taken from the book Vibrations and Waves by AP French. Two objects move around circles, with different angular velocities. The superposition of the two motions merges into one to generate the beautiful Figures of Lissajous. Perfect for exploration of parametric equations. Relevant Courses: Math III, Precalculus, Calculus |
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Simple Harmonic Motion This is a Mathematica application using the LiveGraphics3D applet. An object, apparently going up and down is really moving following a sinusoidal curve. The user can interact with the applet to rotate the box and explore the motion from different angles. Relevant Courses: Calculus |
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Riemann Sums II This EquationPlotter application draws the rectangles representing left sums, right sums, midpoint rule and trapezoidal rule. It also calculates the corresponding approximations. Many features can be changed to satisfy all needs. Relevant Courses: Calculus |
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Slope Fields This EquationPlotter application draws the slope field corresponding to a given differential equation. The user can also plot specific solutions by entering the point on which such solution should pass. Relevant Courses: Calculus |
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Piecewise
Functions This EquationPlotter application draws piecewise defined functions. Six different functions can be plotted at once with the option of plotting additional points or "holes". Asymptotes can also be included by entering their corresponding equations. Relevant Courses: Precalculus |
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Rational
Functions This EquationPlotter application draws Rational Functions. The user enters polynomial expressions for the numerator and denominator, in factored or non-factored form. the program will draw corresponding asymptotes, both vertical or horizontal as well as possible "holes". Relevant Courses: Precalculus |
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2D Inequalities This EquationPlotter application draws inequalities in two dimensions. Many constraints can be plotted at once shading the common solution set. Shading frequency can also be varied to obtain diagrams that are darker or lighter. Relevant Courses: Math 2, Math 3, Precalculus |
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Implicit Plotter This EquationPlotter application draws implicit plots. The equations allowed are polynomial equations in x and y of the form f ( x , y ) = 0. Some basic trigonometric equations are also handled well. Relevant Courses: Precalculus, Calculus |
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Solids Of Revolution This EquationPlotter application draws the solid of revolution generated when a specific region is rotated about a desired axis. Axes of rotation can be any line parallel to either the x or the y - axis. The program will also calculate the volume of the object generated. Relevant Courses: Calculus |
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Solids By Slicing This shows a series of typical solids generated by cross sections with similar properties. This application shows a few examples of such solids, and even though is technically not interactive, the user can still manipulate the objects on the screen. Relevant Courses: Calculus |
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Functions Of Two Variables This EquationPlotter application is a surface plotter. The user can customize the equations and other properties for the plots. the LiveGraphics3D applet is used to provide interaction with the surfaces generated. Relevant Courses: Multivariable Calculus |
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Contour Plot 3D This EquationPlotter application draws a three-dimensional contour plot, i.e., plots a function of three variables of the form W = f ( x , y , z ). the LiveGraphics3D applet is used to provide interaction with the surfaces generated. Relevant Courses: Multivariable Calculus |
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Parametric Plot 3D Typical parametric equation plotter. Draws a three-dimensional plot of a parametrically defined surface or curve. The LiveGraphics3D applet is used to provide interaction with the surfaces generated. Relevant Courses: Multivariable Calculus |
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Tangent Plane This EquationPlotter application is a surface plotter that shows the plane tangent to the surface at a given point. The user can customize the equations and other properties for the plots, including being able to move the tangent plane. the LiveGraphics3D applet is used to provide interaction with the surfaces generated. Relevant Courses: Multivariable Calculus |
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