Getting Started with MATHEMATICA

This short primer consists primarily of a sequence of examples which are intended to illustrate basic features of the mathematical software package MATHEMATICA, which is installed in the Computer Labs on the University of Oklahoma campus. For optimal use, it is suggested that you initiate a MATHEMATICA session and attempt to carry out the examples that are discussed.

1. Starting and Stopping.
   • To start: Sit down at a PC or MAC in any of the A&S Computer Labs and choose MATHEMATICA from the Windows Start menu or icon grouping.
   • To stop: select   Exit   from the File menu in the upper left corner of the MATHEMATICA window.
   • Getting help: There is a very extensive and well-organized Help facility built into MATHEMATICA. This may be accessed by choosing Help Browser... from the Help menu in the upper right corner of the MATHEMATICA window. An even better way to get help is to consult an experienced MATHEMATICA user. The Computer Lab Assistants don't usually fit into this category (but they will if you're working in the Nielsen Hall Lab).

2. Basic Information.
   • Shift-Enter sends input to MATHEMATICA. While MATHEMATICA is compiling the input you will usually see "evaluating" at the bottom of the screen. If "evaluating" remains there for a long time you have probably given MATHEMATICA a problem that involves too many calculations, often you can interrupt the calculation with Alt-+ . Or you can choose "Abort Evaluation" from the "Kernel" menu.
     (Note: Alt-+ means to simultaneously hold down the Alt and + keys. Likewise Shift-Enter indicates simultaneously pressing the Shift and Enter keys.)
   • Return (or Enter) starts a new line on your screen but DOES NOT invoke MATHEMATICA. Use this to keep your lines from scrolling too far to the right, epecially if you are planning to make a print-out of your session.
   • Commands and functions always start with a capital letter. Arguments are enclosed in square brackets " [ ]", not parentheses. For example, try compiling the command Log[1] or ArcSin[1]. Then, for comparison, compile the commands Log(1) and ArcSin(1).
   • Parentheses (round brackets " ( )") should be used to make sure operations work as desired. For example, compare the outcome of 1/2 * 2 with 1/(2 * 2).
   • The percent sign % can be used as a shorthand to denote the last result generated, and %% is the second-to-last result. On the other hand, %7 would represent the output result in the output line number 7, and so on.
   • For WINDOWS users: If previous text is blocked off using the mouse it can be copied using Control-c and then Control-v , after repositioning the cursor where you want to insert the blocked text.
   • A semi-colon " ; " at the end of a line will suppress the MATHEMATICA output. (So MATHEMATICA does the computation but doesn't print it to the screen.)

3. Elementary Functions.
   • Either x * y or x   y (with a blank space inserted between x and y) denotes multiplication of x by y. If you write xy without a space between the x and y then MATHEMATICA will attempt to interpret this as a variable name (and it will NOT interpret it as multiplication). However you can, for example, write 5x to denote 5 * x , but x5 will again be interpreted as a variable name.
   • For exponents, write x^7 for x⁷, and so on.
   • The common constants and e are denoted by Pi and E respectively in MATHEMATICA.
   • Basic elementary functions are invoked by Sin[x], Cos[x], Sinh[x], Sec[x], Tan[x], ArcSin[x], ArcTan[x], Sqrt[x], Log[x], Exp[x], and etc. (The interpretations should be obvious. Note that Log[x] is the natural logarithm function ln(x).)
   • Write N[ Sqrt[2] ] to get an approximation to , or N[ Sqrt[2] , 30 ] to get an approximation accurate to 30 decimal places.

4. Algebra and Calculus.

   Try having MATHEMATICA compile each of the following to see what happens:

   •   Expand[ (x+y+z)^2 ]
   •   Factor[ x^3 + 2x^2 - 5x - 6 ]
   •   Simplify[ Sin[x]^2 + Cos[x]^2 ]
   •   Integrate[ x^5 * Sin[x] , x ]
   •   NIntegrate[ E^(x^2), {x, 0, 3} ]   (This numerically approximates the definite integral .)
   •   D[ Log[x] * Sin[x], x ]   (This computes the derivative with respect to x.)
   •   D[ Log[x] * Sin[x], {x,3} ]   (This computes the third derivative with respect to x.)
   •   Solve[ x^2 + x - 1 == 0, x ] (Note: == is a doubled equal sign, its always used for Logical Equality.)
   •   Limit[ Sin[x]/x, x --> 0 ]   (So MATHEMATICA knows how to apply L'Hospital's Rule!)

5. Fundamentals of Graphing.

   Try having MATHEMATICA compile each of the following to see what happens:

   •   Plot[ Cos[x^2] , {x,-Pi,Pi} ]
     This gives the graph of y=cos(x²) on the interval . You can get MATHEMATICA to enlarge the picture by first clicking on the graphic output and then dragging one of the little black rectangles while holding down the left mouse button.
   •   Plot[ Cos[ x^2 ] , {x, -Pi, Pi}, PlotRange -> { 0,1 } ]
   •   Plot[ Cos[ x^2 ] , {x, -Pi, Pi}, AxesLabel -> {"x-axis", "y-axis"},
         Frame -> True, PlotLabel -> {"My graph"} ]
   •   Plot3D[ x^2 - y^2 , {x, -3, 3}, {y,-3,3}]

   More details on controlling the output of the "Plot" command can be found on the 2-dimensional plotting page. Graphing functions of two variables is discussed on the "Plot3D" command page.