This Vector Calculus (VectCalc)
software was designed as a help to understand graphs and contour
plots of functions of two variables, as well as functions of two
variables obtained as cross-sections of functions of three variables.
The following is a description of the package, which is a Graphic
User Interface for the Student Edition of MATLAB 5. If you have suggestions
or comments about this package, please send an e-mail to
lega@math.arizona.edu .
Installation
To install the software on your computer, copy the following files
Getting started
To use VectCalc, start a MATLAB
session and type
VectCalcat the MATLAB prompt. The window of the form shown below appears. It is referred to as the MATH 223 Main Window.
- In the left box, you can select functions of two or three variables to look at. Here "Hyperboloid" has been selected.
- The right box contains a short description of what the software allows you to do and tells you how to start.
- Click the bottom left button if you want to QUIT VectCalc and return to the MATLAB Command Window.
- Click the bottom right button to PLOT the function highlighted in the left box.
Functions of two variables
If you select any function listed under
FUNCTIONS OF 2 VARIABLESand then click the PLOT button, the 2D Plot Window pops up:
When you start, the graphic box always shows the graph of the function of two variables which has been selected. The name of this function appears above the plot. By clicking and dragging the mouse on the graph, you can rotate the figure. The buttons at the bottom allow you to do any of the following:
By clicking on any of the contour curves, the value of the function on that curve will be marked on the plot. Once you are done marking the level curves, hit the Enter key to finish the plot. These instructions also get printed on the MATLAB Command Window when you start the contour diagram.
This is the same as a contour plot, except that the value of the function at a given point is indicated by the color of the plot at this point.
In this picture, because of the restricted size of the contour diagram, you will not be able to label the level curves. However, a contour diagram is shown at the bottom of the graph of the function, to illustrate how these two plots are related.
Functions of three variables
If you select any function listed under
FUNCTIONS OF 3 VARIABLESand then click the PLOT button, the 3D Plot Window pops up:
At first, this window always shows the graph of the function of two variables obtained by slicing the function of three variables which has been selected, along the plane x = 0. The name of the selected function appears above the graphic box.
