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4434Exploring Multivariable Calculus
http://www.merlot.org/merlot/viewMaterial.htm?id=437177
The main goal of this project is to improve student understanding of the geometric nature of multivariable calculus concepts, i.e., to help them develop accurate geometric intuition about multivariable calculus concepts and the various relationships among them.To accomplish this goal, the project includes four parts:· Creating a Multivariable Calculus Visualization applet using Java and publishing it on a website: web.monroecc.edu/calcNSF· Creating a series of focused applets that demonstrate and explore particular 3D calculus concepts in a more dedicated way.· Developing a series of guided exploration/assessments to be used by students to explore calculus concepts visually on their own.· Dissemination of these materials through presentations and poster sessions at math conferences and through other publications.Intellectual Merit: This project provides dynamic visualization tools that enhance the teaching and learning of multivariable calculus. The visualization applets can be used in a number of ways:- Instructors can use them to visually demonstrate concepts and verify results during lectures.- Students can use them to explore the concepts visually outside of class, either using a guided activity or on their own.- Instructors can use the main applet (CalcPlot3D) to create colorful graphs for visual aids (color overheads), worksheets, notes/handouts, or tests. 3D graphs or 2D contour plots can be copied from the applet and pasted into a word processor like Microsoft Word.- Instructors will be able to use CalcPlot3D to create lecture demonstrations containing particular functions they specify and/or guided explorations for their own students using a scripting feature that is being integrated with this applet.The guided activities created for this project will provide a means for instructors to get their students to use these applets to actively explore and “play” with the calculus concepts.Paul Seeburger, the Principal Investigator (PI) for this grant project, has a lot of experience developing applets to bring calculus concepts to life. He has created 100+ Java applets supporting 5 major calculus textbooks (Anton, Thomas, Varberg, Salas, Hughes-Hallett). These applets essentially make textbook figures come to life. See examples of these applets at www.monroecc.edu/wusers/pseeburger/.Broader Impacts: This project will provide reliable visualization tools for educators to use to enhance their teaching in calculus and also in various Physics/Engineering classes. It is designed to promote student exploration and discovery, providing a way to truly “see” how the concepts work in motion and living color. The applets and support materials will be published and widely disseminated through the web and conference presentations.Demos with Positive Impact
http://www.merlot.org/merlot/viewMaterial.htm?id=80956
Demos with Positive Impact is a collection of quick classroom demos that enhance the learning of mathematics content through animations, experiments etc. Each demo comes with stated objective, prerequisites, instructor notes and platform info, plus the level of the demo and credits. This setup appears conducive to quick inclusion into a class. To view a video of the award winning author, go to http://about.merlot.org/Videos/Math_Demos/Math_Demo.html" target=״_blank״>Demos with Positive Impact - the Mathematics Award Winner 2008 videoThe author also participated in the MERLOT Classics Series on Elluminate: " target=״_blank״>https://sas.elluminate.com/site/external/jwsdetect/playback.jnlp?psid=2010-03-25.1727.M.9E9FE58134BE68C3B413F24B3586CF.vcr Flash Mathlets
http://www.merlot.org/merlot/viewMaterial.htm?id=87515
״The Flash mathlets are divided into two sections.The For Students and Instructors section contains Flash applets which may be useful to instructors for classroom demonstrations, as well as to students for independent work and exploration. The For Developers section presents applets together with varied templates and the complete, object-oriented, easily-customizable source code that can be used by instructors for creating their own customized versions of the applets.״Mathlets: JAVA Applets for Math Applications
http://www.merlot.org/merlot/viewMaterial.htm?id=88565
Collection of JAVA applets for precalculus, calculus, graphing, three-dimensional graphingAnimations (for freshman and sophomore calculus and differential equations)
http://www.merlot.org/merlot/viewMaterial.htm?id=82071
This is a collection of animations which I found to be helpful demonstrations in freshmand and sophomore calculus and differential equations classes. For most animations, MathCAD code is available.Eric Weisstein's World of Mathematics
http://www.merlot.org/merlot/viewMaterial.htm?id=76247
This site provides an extremely large encyclopedia-style collection of material related to mathematics at the college level and beyond. Much of the material deals with advanced topics. A large number of animated GIFs and java applets are presented as visual aids and the site has won numerous web awards. The World of Mathematics is hosted by Wolfram Research, Inc., and is offered as a free service to the mathematics community.Function Grapher
http://www.merlot.org/merlot/viewMaterial.htm?id=89592
Graphs one or more functions of a single variable, with zoom in/out and other nice features.How the ball bounces
http://www.merlot.org/merlot/viewMaterial.htm?id=77011
An animation portraying the mathematics of a bouncing ballNumerical integration simulation
http://www.merlot.org/merlot/viewMaterial.htm?id=75032
This is a Java-enhanced tutorial that allows students to learn about the rectangular, midpoint, and trapezoidal methods of numerical integration.Surface Plotter
http://www.merlot.org/merlot/viewMaterial.htm?id=88968
A Java applet which allows one to sketch surfaces given byz = f(x,y).