Part I. The Mathematica Notebook

Section 1. Cell structure: Input/Output

0. Pull down the Help menu, choose Tutorial and work through it.
Open a new Mathematica Notebook and do the following.
1. Reduce the fraction 546/1001 to lowest terms by typing

546/1001

and pressing [Enter]. This is referred to as executing the entry.

2.* Simplify the square root of 19,220 by entering and executing

Sqrt[19220]

Then obtain the integer factorization of 19220 by entering and executing

FactorInteger[19220]

The output means that 19220 = 2^2 * 5 * 31^2

3. * Obtain the integral of the expression e^(3 x) cos(2 x) sin(4 x). You may enter it into the Integrate function as follows

Integrate[  Exp[3x] Cos[2x] Sin[4x],  x ]

4. Pull down the Format menu. Choose Style Sheet/Natural Color. Experiment with some of the other styles. Note. This Manual was written using the TutorialBook style.

5. Restore the Style to the original TutorialBook style. Save it with the name "MyFirstMathematicaNB".

Section 2. Mixing Text and Mathematics

1. Open a new Mathematica Notebook. Pull down the Format menu, choose Style/Text (Command-7 on a Macintosh, Control-7 on a PC) and type your name. Press the return key and type the date. Press the down arrow, then Command-7, and type Mixing Text and Mathematics. Note that this appears in a new text cell. Now press the down arrow,/Command-7 combination one more time, and type the following sentence:

This Notebook contains examples of text cells like these and input/output cells like the following.

2, Press the down arrow to get an Input cell and define the variable y as a function of x by typing y = Sin[x] and pressing [enter]. Sin[x] appears as the output.

3. Before continuing, use the mouse to select the third text line at the top of the worksheet,  "Mixing Text and ....". Then pop down the menu of paragraph and text styles on the left side of the Context bar and choose the paragraph style named Title.  

4. Go back down the Notebook and click the mouse in the white area below the last entry and define z as the derivative of y with respect to x by entering and executing z = D[y,x]

5. When the new output cell appears there will be a line across the page and the paragraph style should be Input. Press Command-7 to change it into a text cell and type the following:

z is the derivative of y. Both z and y are plotted below. Which one is which? How can you tell?

6. Press the down arrow to get an input cell and graph y and z as functions of x by executing the entry

Plot[ {y,z}, {x,0,6} ]

Note that both curves are black.

7. Click the mouse after {x,0,6} and type a comma followed by

PlotStyle -> {RGBColor[1,0,0],RGBColor[0,0,1]}

Press [enter] to execute the Plot function again. The y-curve is red and the z-curve is blue.

8. Click in the white space below the graph if necessary, press Command-7 and type in your answers to the questions asked above.
9. Save this Notebook with the title "My2ndNotebook".
10. Quit Mathematica.
11. Open the Notebook you just saved by double clicking on its icon.
12. Pull down the Kernel menu and choose Delete All Output.
13. Pull down the Kernel menu again and choose Evaluation/Evaluate Notebook. This puts the information in the Notebook back into the Mathematica kernel.

14. With the mouse, click in the white region below the last cell and define the variable Y as an antiderivative of z with the following entry Y = Integrate(z,x) .
15. Press the down arrow and Command-7. Then type the following:  

Well, that wasn't hard. Now I now how to enter text and  mathematics in Mathematica.

16.* Save your Notebook (Command-S) then print it.


Created by Mathematica  (December 6, 2004)