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 or  Expressions ) 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  ENTER 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 or Draw or Execute will start the program running. In some of the graphing programs, you also have to  click a point in a picture to specify a starting point.

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.

FUNCTION EXPRESSIONS

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 of   y.

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.

Operations/Functions	Meaning
+, -, *, /	add,subtract,multiply,divide
^	exponentiation  ( a^b  is  ab)
abs(x )	absoluate value of x
sqrt(x )	square root of x
ln(x)	natural logarithm of x
exp(x)	ex
sin(x), cos(x),tan(x)	sine, cosine, tangent of x (x in radians)
asin(x),acos(x),atan(x)	arcsine, arccosine, arctangent of x (x in radians)
H(x)	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 and subtractions.

The * (asterisk) for multiplication may be omitted in products of a  number and a variable, and in products of expressions that are both  in parentheses.

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.