Jason
McCullough
Department of Mathematics
University of California - Riverside
900 University Ave.
Riverside, CA 92521
Email: jmccullo AT math.ucr.edu
Office: 227 Surge Hall
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Jason
McCullough
Department of Mathematics University of California - Riverside 900 University Ave. Riverside, CA 92521 Email: jmccullo AT math.ucr.edu Office: 227 Surge Hall |
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| Home Professional Information Research Teaching Commutative Algebra Notes Geogebra Demos  Links |
Below I have some of the Geogebra demos I have created or modified and used in various classes. They are viewable in any browser as long as you have an up-to-date version of Java run-time environment installed. Feel free to use them for whatever noncommercial use you please. Comments/error reports are welcome.Trigonometry:Sin(x) Demo - Sin(x) and the unit circle. Cos(x) Demo - Cos(x) and the unit circle. Arcsin(x) Demo - Definition of Arcsin(x). Arccos(x) Demo - Definition of Arccos(x). Arctan(x) Demo - Definition of Arctan(x). Differential Calculus:Motivation for Limits - Graphs and traces values for the function f(x) = sin(x)/x to motivate the idea of the limit of a function. Limit Demo 2 - A jump discontinuity. Limit Demo 3 - An infinite discontinuity. Limit Demo 4 - A tricky example: f(x) = sin(pi/x). Epsilon Delta Definition of a Limit - Shows how the formal definition of a limit looks visually and allows students to pick deltas for various epsilons. Epsilon Delta Demo 2 - The function f(x) = sin(x)/x. Epsilon Delta Demo 3 - The function f(x) = 1 if x>0 and 0 if x<0. Defintion of the Derivative - Shows the derivative as the limit of slopes of secant lines. The derivative as a function - Traces out the derivative by recording the slope of the tangent line at various points. 1st Derivative Test - Relates a function to its first derivative to show where f(x) is increasing and decreasing. 2nd Derivative Test - Relates a function to its second derivative to show where f(x) is concave up and concave down. Implicit Differentiation - Measures the slope of the tangent line to an ellipse to motivate implicit derivatives. Asymptote Demo 1 - Shows a function along with its asymptotes to help visualize infinite limits. Asymptote Demo 2 - Same as the previous demo but with a different function. Integral Calculus:Definite Integrals and Riemann Sums - Fully customizable demo to illustrate definite integrals and approximation by various Riemann Sums or by the Trapezoid Rule. Motivation for the FTC - Graphs f(x) = x and the definite integral of f from 0 to a moveable point x. Area Between Two Curves Area Between Two Curves 2 - Considers the Case when one function is negative. Definition of the Natural Logarithm as an Integral - Links ln(x) to the integral of 1/x. Derivative of Arctan - Compares d/dx arctan(x) with 1/(1 + x^2). Defintion of Sinh and Arcsinh. Defintion of Cosh and Arccosh. Defintion of Tanh and Arctanh. Hyperbolic Functions and the Hyperbola x^2 + y^2 = 1. - Shows how (cosh(t), sinh(t)) parameterizes a hyperbola. Simpson's Rule - Fully customizable demo to illustrate definite integrals and approximation by Simpson's Rule. Improper Integral (Type 1) - Investigates the integral from 1 to infinity of f(x). Improper Integral (Type 2) - Investigates the integral from 0 to 1 of f(x) where f(x) has an infinite discontinuity at 0. Sequences and Series:Growth Rates of some common functions - A primer for limits at infinity. Integral Test Demo - Shows the integral test comparison for the series 1 + 1/4 + 1/9 + 1/16 + .... Taylor Polynomial Demo - Customizable graph of any function along with its nth Taylor Polynomial at a point. Differential Equations:Euler's Method Demo - Shows the direction field for the differential equation y' = y and the first few iterations of Euler's Method for various jump sizes. Geometry:The following demos were created by my Math 133 students in the Winter Quarter of 2011. Theorem of Pappus - by Michael Bauders Theorem of Desargues - by Michael Kim Projective Version of the Theorem of Pappus - by Kirandeep Gahir Projective Version of the Theorem of Desargues - by Davis Gibson Angles in a Circle Theorem - by Mark Zimmerman Pythagorean Theorem - by Maria Mosqueda Constructing the Incircle - by Siri Tirumalasetty Constructing a Regular Pentagon - by Leo Vu and Benjamin Li Constructing a Tangent to a Circle - by Emily Muhu Euclid's Proposition IV.10 - by Ariana Garcia Squaring the Rectangle - by Janet Godinez Concurrence of Altitudes and Medians of a Triangle - by Gary Deluna The Euler Line - by Reanna Gibbs and BiJon Clark The Nine Point Circle - by Brian Baltazar Matrix Representation of a Rotation - by Scott Manifold The Three Reflections Theorem - by Elizabeth Morlock and Kaitlin Giacalone |