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CalcPlot3D 
Course Topic(s): Multivariable Calculus | Vector Fields and Flowlines | Taylor Polynomials, Hessian | Directional Derivatives and Gradients | Partial Derivatives, Differentiability | Graphing Multivariable Functions | Properties of Curves | Conic Sections & Quadric Surfaces | Lines and Planes | General Tools
This part of the tool allows the user to graph any surface in 3D and then plot the Taylor Polynomial of degrees 0 through 5. Both the algebraic equation and the graph are given of the Taylor Polynomial. The user can set the center point of the polynomial and can use a slider to change from degree to degree. CalcPlot3D also contains a parametric surface graphing capability, including the ability to display a "trace" point on the surface.
Resource URL: http://web.monroecc.edu/manila/webfiles/calcNSF/JavaCode/CalcPlot3D.htm
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Subject classification(s):
Limits
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Functions of Several Variables
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Several Variable Calculus
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Calculus
Creator(s): Paul Seeburger
Contributor(s): Paul Seeburger
This resource was cataloged by Larry Green
Publisher:Exploring Multivariable Calculus
Resource copyright: Paul Seeburger
This review was published on June 09, 2011
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thread #1:
Ways you have used CalcPlot3D
I would love to see some comments added to this resource to reflect the ways many instructors have used this applet in their teaching. I created this resource to help my students to see the connections between the concepts we study in multivariable calculus more clearly. I use it to demonstrate certain properties in my lectures like the fact that the gradient vector points in the compass direction we should move along a surface in order to go most steeply uphill. I also use it in lectures to visually verify solutions to various boardwork exercises like finding the equation of the plane determined by three non-collinear points and the intersection of two planes (or other surfaces). I then get my students to use the applet by requiring them to visually verify solutions to various homework problems on graded worksheets. They print out their resulting graphs from the applet and hand them in with their homework. I have them do this with various topics including those mentioned above, as well as contour plots, level surfaces, tangent planes, flowlines through vector fields. I also ask my students to complete several concept explorations that use the applet to consider the geometric properties of dot products, cross products, velocity and acceleration vectors, and Lagrange multiplier optimization. I use it for some "what-if" types of explorations in class when we study space curves as well. I would love to hear what others are doing, and in particular, I think it would be helpful to share particular functions, space curves, etc. and activities that could be done by students using this applet (or similar resources).