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Visualizing
Concepts in Multivariable Calculus
The authors of our textbook, Richard Williamson and Hale
Trotter have inspired numerous
Java applets which assist in the visualization of the concepts of
multivariable calculus.
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Visualizing
Arithmetic Operations on Vectors
Here is an applet which allows you to see user-provided examples
of vector addition, subtraction and vector dot product.
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Visualizing The
Vector Cross Product
This applet from Syracuse indicates how the vector cross product can
be visualized and connects it to planes in R3.
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Collection
of Flash-based Tools for Multivariable Calculus
These are Barbara Kaskosz's
Flash-based tools which plot parametric
curves, parametric
surfaces, and 3-d
surfaces.
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Interactive
Gallery of Quadric Surfaces
This article at the Journal of Online Mathematics and its
Applications by Jonathan
Rogness allows the user to interactively view (from any angle!)
how quadric
surfaces depend on their parameters.
- Visualizing
direction fields and solution curves
This website allows for visualization of simple direction fields.
Numerically brittle.
- Fancier program for
visualizing
direction fields
This website (requires installation of Java 1.1.6) and uses DFIELD
to show direction fields and solution curves.
- 2-Dimensional
Newton's Method Applet
This website demonstrates what Newton's Method in
two-dimensions would look like.
- MathsHelp:
Working With Vectors
A very cool website which discusses vector equations of planes
and lines
well as other useful operations with vectors such as the vector
cross product and dot
product.
- Winplot:
Free Software For Visualizing 2-D and 3-D Objects
This software works in any Windows platform.
- Vector Field
Analyzer
This very cool java-based applet allows one to visualize vector
fields, as well as make several related computations.
- Paul Falstad's
Vector Field
Simulator
This very dynamic, animated java-based applet allows one to
simulate actual vector fields. It has a number of defined 2-D
fields as well as allowing for user-defined fields. It also computes
the curl and divergence of the 2-D fields, illustrating Green's and
Stokes' Theorem. There is a
limited 3-D version and many other cool "mathlets" at Paul
Falstad's website.
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