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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.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.״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).Vector Fields Simulation
http://www.merlot.org/merlot/viewMaterial.htm?id=75572
This applet demonstrates various properties of vector fields. You can select from a number of vector fields and see how particles move in the field if it is treated as either a velocity or a force field. This helps you visualize the field. Also you can see the values of the divergence and curl of the field. [From Author's Description]A Parameterized Curve Applet
http://www.merlot.org/merlot/viewMaterial.htm?id=241454
This site contains an applet that allows the user to define a parametrized 2-dimensional curve and then create a three dimensional graph of this curve. Some additional properties of the curve can also be shown on the graph. This site is a member of the Saint Louis University Calculus collection .Connected Curriculum Project - Materials for Precalculus
http://www.merlot.org/merlot/viewMaterial.htm?id=84777
The CCP includes modules that combine the flexibility and connectivity of the Web with the power of computer algebra systems such as Maple, Mathematica, MatLab and MathCad. The single-topic units can be used for a two-hour lab, or for a shorter supervised period with follow-up on the student's own time, or for self-study. Modules are organized into areas of precalculus, differential calculus, integral calculus, multivariable calculus, linear algebra, differential equations and engineering mathematics. Applications include those in biology, chemistry, physics, engineering, economics and environmental science.Cross Section Applet
http://www.merlot.org/merlot/viewMaterial.htm?id=241424
This module is a part of the Saint Louis University collection of Calculus applets. The site contains an applet that is designed to show how the graph of a function in two variables can be constructed from the cross sections, which are each graphs of one variable.LiveGraphics3D
http://www.merlot.org/merlot/viewMaterial.htm?id=86761
LiveGraphics3D is a non-commercial Java 1.1 applet that enables users to put almost any three-dimensional graphics computed by Mathematica directly onto an HTML page. It can then be viewed and interactively rotated without any additional software. LiveGraphics3D also shows animations and supports parametrized graphics.Vector Field Applet
http://www.merlot.org/merlot/viewMaterial.htm?id=91106
This applet draws a vector field and generates integral curves at the click of a mouse.Least Squares Applet
http://www.merlot.org/merlot/viewMaterial.htm?id=314427
Quoted from the site: This applet explores fitting a polynomial p(x) of degree n to a given set of data points. It computes the best least squares approximation to the data, "best" in the sense that SUM (p(xi) - yi)^2 is minimized. The applet provides controls for choosing the degree n, setting the precision of all displayed numbers, selecting and deselecting data points, and editing the data list. It also allows for entry of your own custom polynomial and computing its least squares error.