Instructions for Running Interactive
Activate a program by clicking on its name in the list.
An "Instructions" window will appear, with information on what the program
does and how to use it. To remove the window, click the OK
button at the bottom of the window.
Each program displays several buttons. Clicking on one of them
(for instance, Limits
) will open a window displaying sample values for program parameters,
or expressions defining functions for the program to use. You can
change these values and expressions so they define the problem you
want to investigate.
After setting the values you want in a window, click the window's
button to tell the program to use the values you have
set. THIS STEP IS ESSENTIAL, otherwise the program will not take account
of your values.
After you have entered the data to set up the problem, clicking on
the button labelled Compute
will start the program running. In some of the graphing
programs, you also have to click a point in a picture to specify a
All the programs are set up with resonable sample inputs. The
first time you run a program you may want simply to call up the entry
window or windows and click "Enter" without making any changes, just
to see what the program does.
The 3D graphics in the multivariable calculus applets can be rotated by dragging
the mouse over the graphics. Click on the Draw
button to return the figure to its original position.
Each program involves one or more of the variables t, x, y, and z.
In the programs concerned with second-order differential equations,
the variable z is used also to stand for y', the derivative
The functions are defined by expressions made up from numerical constants
and the variables allowed in a particular program combined using the
operations and functions listed below.
|+, -, *, /
| exponentiation ( a^b is ab)
|absoluate value of x
|square root of x
|natural logarithm of x
|sine, cosine, tangent of x (x in radians)
|arcsine, arccosine, arctangent of x (x in radians)
| Heaviside function of x, defined by
H(x) = 0 for x< 0
H(x) = 1 for x>=0
Terms may be grouped using parentheses, and the usual order of operations
is followed, with multiplications and divisions done before additions
The * (asterisk) for multiplication may be omitted in products of a
number and a variable, and in products of expressions that are both
If the program can't interpret an expression you have typed, it brings
up a window to tell you so and invites you to try again. Some possible
reasons for rejecting an expression are:
- parentheses not properly matched up.
- use of a variable not allowed for a particular program.
- typing errors such as a comma for a decimal point, which
may be hard to distinguish on the screen.