- Sit in front of the machine: -- This may seem silly, but the first thing is to make sure that you are sitting in front of the {proper} machine. You want the machines in room G25 labeled Gateway (any of these will do).
- Type in your username, password: -- From the computer's point of view, you have an identity that is a string of symbols. In order to get the machine's permission to do anything, you need to tell the computer who you are. Thus, the first thing you should do is to type your username. A typical username is your first initial (as it appears on the official roles) together with enough of your last name to make 8 letters. Jane Smith would have the username jsmith and Harold Williamson would have the username hwilliam. There will be exceptions for common names, and I will tell you if it is any different than this. Once you have typed the username, hit the Tab key. You will then be asked to type a password. This is to make sure that noone else can pretend to be you. Your initial password is ntxxxx, where the xxxx is the last four digits of your student id.
- Double click on the Mathematica icon with the left mouse button. After a few seconds, you will see a Mathematica window on your screen. This is where you will do your work. You are now ready to do some mathematics on the computer!

- Defining a function: -- Suppose you want to input the function
$f(x) = 7x^5 + \sqrt{x^2 - 1}$. In the Mathematica window that you have on
your computer screen, you will type the following exactly as it appears:
f[x_]:=7 x^5 + (x^2 - 1)^(1/2)

Once you have typed this in exactly this form, hit the (Shift) Return key to "execute" the definition. Note several things about this definition. First, note that there is a subscore next the the variable x in the square brackets. To do this, you hold the shift key down and type the - key next to the 0. This tells the computer that you will allow numbers to be put into the function. Also notice that there is a colon before the equal sign. This must be there in order for the computer to know how to apply the function later on. Whenever you multiply a number times a variable, you have to leave a space between them. Anything raised to a power will use the symbol \^\ . As mentioned in class, we will often use letters other than f for our functions and variables other than x for the independent variable, but any definition of a function will follow this basic form. - Plotting the function: -- Once you have defined a function, type the following command:
Plot[f[x],{x,-10,10}]

As before, to "execute" the command, you need to hit the (Shift) Return key on the right hand side of the keyboard. If your function has a different name than f[x], then use that in place of f[x]. The range that I have listed (from -10 to 10) is only for this example. You will often have to change those to focus in on the part of the graph that you need to see in order to answer the question. If you do not like the picture that you see, then you can use your mouse to go up to this range, and delete and replace those numbers with other numbers that you think will give you a better picture. You may have to repeat this several times: once you have made the changes, hit the (Shift) Return key to see what the new picture looks like. If you think you want more than one picture of the same function, then simply retype the command (or use cut and paste if you know how) to do the whole command again with a different range. - Solve a function: -- We will primarily use this command to find out where
certain functions are equal to 0. As we will see this semester, knowing
where functions are 0 often tells us important information about the problems
we are trying to answer. Once you have the function defined (if you have not
done this, go back to that step!), type the following command:
Solve[f[x]==0,x]

Once you have it in this form, hit the (Shift) Return key to execute the command. If you are working with a different variable than x, then replace both x's in the command above with the appropriate letter. Notice that there are two = signs in the command: make sure you always do that for the Solve command. This will give you every solution to this equation, but sometimes they will not be in a form that you recognize. Often, it is useful to use the commandN[%]

to get an exact value. There are other ways to get exact values, and you are welcome to experiment with Mathematica to see the best way to do things. - Integrate a function: -- Type the following command:
Integrate[f[x],x]