A First Encounter with Scientific Notebook

Don Allen

Department of Mathematics

Texas A&M University

and

with liberal assistance from the

Scientific Notebook Help Menus

Abstract. We study the capabilities of a scientific software package to produce clean, clear, typeset mathematics with a minimum of effort.

Introduction

To enter the heading Introduction, type the word ``introduction'' on a new line. Then with the insertion point on that line, choose the Heading 2 from the Section/Body Tag list on the Tag Toolbar (at the bottom of the window).

Tagbar (bottom of SNB screen)

Now lets's make a few points. \underline{First press enter} at least once. From the Item Tag list on the Tag Toolbar, choose the Numbered List selection. You should see ``1.'' on the line.

Type your name: S. N. Book. Make your last name bold. Choose Bold from the Text Tag list on the Tag Toolbar. S. N. Book. Now press enter.
You should see the number ``2.'' on the current line. \underline{Enter your address}. Now press enter again.
Do you see the number ``3.'' ? \underline{Enter your office phone}. By the way the left quote mark is made with the symbol `. Press it twice.
Finally, if you'd rather have lettered item rather than numbered, you can change the setting in the Edit/Properties menu. (at top)
You can apply the Emphasized, Strongly Emphasized, Keyboard Input, Sample Text, Bold, Italics, Typed Code, Bigger, and Smaller tags by selecting text, then choosing the Text Tag from the Tag Toolbar at the bottom of the Scientific Notebook screen.
Turn off the numbering in the Item Tag list or by choosing the Remove Item Tag from the Tag Toolbar.

Toolbars

Make sure that all your toolbars are displayed. We assume that in the following lessons. From the View menu select the Toolbars option. Check all the boxes. This will eat up some screen real estate, but by-and-by you can decide which of them you really don't need or want.

Entering Math

Easy to produce, great appearing math is the forte of SNB. You can make fractions, radicals, integrals, subscripts, superscripts, almost anything you can conceive of with just a few keystrokes. Let's try it. The most important thing to remember here is that there is Math Mode and Text Mode. At the top of the SNB screen you should see that you are in Text Mode by the button. Choosing it gives and you're in Math Mode.

A quadratic. Superscripts and subscripts.

So choose the math mode now. Enter some math, just by typing it in. For instance: $\ 2x^{2}+3x+2=0$ How did we get $x^{2}$ ??? To get that you need to type the and then the superscript button at the top. So, you type and then $\rightarrow$ from your keyboard to get out of superscript mode. Choose to get out of math mode. Now type in some math using a subscript.(Don't forget to use the subscript button For example: $a_{ij\text{ }}$ or a $_{i_{j}.}$ Even subscripts of subscripts are possible.

Exercise

Try typing the following:

1. $2^{p}-1$
2. Fermat numbers: $2^{2^{p}}+1$
3. $x^{3}+a_{0}\,x$

Fractions and Radicals.

Fractions and radicals are easy to make. You need to spot the Fraction button and the Radical button at the top of your screen. Try to type the expression.
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Here are some directions for fractions. Directions for radicals are similar.

Choose . Type the numerator.
Move to the denominator by pressing the down arrow or the Tab key, or by clicking on the denominator input box.
Type the denominator.
Press the right arrow or the spacebar to leave the fraction.

The following example is more complex. Can you get it?
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Notice in this expression there is a fraction in a fraction. Just use the Fraction button anytime you need it, no matter where you are. Also you see the cube root, not square root. $\$ To get it, just place the insertion point where the root should be and type the root you want. $\$ Here's one. $\$ Try to get it.

Displaying mathematics.

Just above you see the functions and $H\left( x\right)$ displayed. This is easy to achieve using the Display button Choose now. Type a mathematical expression in the display, or select a piece of mathematics and drag it into the display. Note the following:

Inserting enter immediately before a display will add extra vertical space. If you do not want this space, place the insertion point immediately before the display and press backspace. Inserting enter immediately after a display will add extra vertical space and cause the next line to start a new paragraph. If you do not want this space, place the insertion point at the start of the next line and press backspace.

Now enter some mathematics of your own choosing in a displayed format. Examples:
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Here, we've used Greek letters for the first time. Find them by choosing the lowercase Greek button or the uppercase Greek button on the Symbol toolbar Notice also the different appearance of the trig functions. SNB knows these functions and changes the font to normal, just like in textbooks. Finally, by choosing Enter within Display mode, you get a new line. \underline{Equality signs automatically line up}.

More Math (Making Graphs)

Making a graph is one of the most powerful of the SNB options. From the simplest display of straight line to a complex multiplot, making graphs is remarkable simple.

Example

(A simple graph) In Math mode, type an function (or even equation), say Place the insertion point anywhere in the expression and press the Plot Rectangular button

What I did here was select Example from the Item tag list on the Tag Toolbar and then choosing Center from the Section/Body Tag list on the Tag Toolbar. So, we have a simple plot.

Example

2. (Using Plot Options) Make a label on the plot which says, ``My first plot'' ; remove the box around the plot; make the plot thicker and red; and finally restrict the horizontal axis to

Four things to do; four steps are required. Click anywhere in the plot. There should appear six ``handles'' around the plot and a small blue box in the lower right corner. Click the small blue box. This opens the Plot Properties dialogue box. To make the label, choose from it the Labeling tab and enter the caption ``My first plot'' in the Caption box. Press OK. For the second task, open again the Plot Properties dialogue box. Selecting the Frame tab, choose the Content only button. For the third task, open again the Plot Properties dialogue box. From the Plot Components tab select Line Color as red and Thickness as medium. For the last task, select the View tab and (un)check the Default box. Then, enter the new range for the -components. Click inside the respective boxes. Striking the Tab key takes you from the left limit to the right limit. Your new graph should be just as below.

My first plot

Exercise

Make a plot of the function $\sin x^{2},$ with a label `` $\sin x^{2}'.$ Make the horizontal range the vertical range the color blue, and the thickness medium. Change the number of -axis ticks to 7 and -axis ticks to 5. (For this one you need to select the Axes tab in plot properties.) Center the graph on the page. You should get the graph below.

$\sin x^{2}$

There are often multiple ways to access various menus. The help manual is the best source of these. For example by selecting Edit/Properties, you can also access the Plot Properties dialogue box

Example

3. (A complicated graph.) Use Plot 2D + Rectangular to plot the graph of

$x\sin \dfrac{1}{x}$

Add the Label by typing it into the Plot Properties + Labelling tabbed dialog in the Caption Text entry field.

To add an expression to a 2D plot

Select the expression with the mouse and drag it onto the plot.

Plot 2D + Rectangular

$x\sin \frac{1}{x}$

Select and drag to the frame (one at a time)

and

Revise Plot Components page, Item Number : 2, Line Color: Red, Item Number: 3, Line Color: Blue

You can also add expressions with Add Item in the Plot Properties tabbed dialogs, as described earlier.

Making a hypertext link.

Making hyperlinks is a easy as typing in what it is. For example if you want your students to read the headlines from the on-line newspaper USA Today, you can hyperlink it

1. With the mouse choose what you want hyper linked.
2. Select the Hyperlink button.
3. Type into the target box the link: http://www.usatoday.com.
4. You have USA Today
5. Finally, if you choose some linked text, copy it, and then paste it somewhere else in your document, the link comes along.

Exercise

On your worksheet enter a hyperlink to your own home page or some other URL.

Making hypertext links to a point within a file is also easy. For such links you need a marker tag at the URL. For illustration purposes, use the document you have been creating.

To create a marker

Place the insertion point in the item you wish to mark.
Click , or from the Insert menu, choose Field, and then choose Marker.
Enter the key for the item.

Use only letters, numbers and the following characters: : ; , . ? ! \lbrack \rbrack ( ) `` $\sim$ - / *
If you want to display a list of the keys defined for your document, click the arrow next to the Key box, then scroll the list.
Choose OK.

Making hypertext links (general case).

To create a hypertext link

Click , or from the Insert menu, choose Field and then choose Hypertext Link.
In the Screen Text box, enter the text of the link as you want to see it on the screen and in print.

In the Target box, enter the address of the targeted item. The format of the address varies with the target, as shown in these examples:

The address	Links to
here	the marker here in the current document
yourdoc.tex	the document yourdoc.tex in the current directory
c:\other\yourdoc.tex	the document yourdoc.tex in the other directory
yourdoc.tex#here	the marker here in the document yourdoc.tex
http://www.site/doc.html	the information at the web address http://www.site/doc.html
http://www.site/doc.html#here	the marker here at the web address http://www.site/doc.html

Choose OK.

Doing Math with Maple

You and your students will be delighted with how simple routine mathematical calculations, symbolic or not, can be when you use the Maple engine contained in Scientific Notebook. For doing mathematics the Computebar contains the basic buttons to do most jobs.

To evaluate an expression, place the insertion point anywhere in the expression and press the Evaluate button .

Example

Let's evaluate a number. Place the insertion point in the expression and choose the Evaluate button to get Notice that the exact answer is given, not some decimal approximate.

To \underline{numerically} evaluate an expression, place the insertion point anywhere in the expression and press the Evaluate Numerically button

Example

\underline{Numerically} evaluate the number. Place the insertion point in the expression and choose the Evaluate Numerically button to get
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Exercise

Evaluate and also evaluate numerically the following: (Don't forget to use Math mode.)

$\sqrt{2+36}$
$\pi$

To expand an expression use the Expand button .

Example

Expand the expression Place the insertion point in the expression and choose the Expand button we get

Exercise

Expand the following:

Note what happens to the numerical coefficients. You get the full expansion.

To simplify an expression use the Simplify button .

Example
Simplify the expression Place the insertion point in the expression and choose the Simplify button to get

Example
Simplify the following:

A little calculus --- derivatives

To differentiate a function write the expression where $f\left( x\right)$ is the function to be differentiated.

Example

Find Just type in Math mode (of course),place the insertion point within the expression, and choose the Evaluate button. We get
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Note if you evaluate an expression in display mode, the answer will appear on the next line. You will have to move it into the display if that is where you wish it to be.

Exercise

Find the following derivatives:

Yes, indeed, you can compute higher order derivatives directly. You can also use any variable. Use SNB to evaluate You will get zero, just like you should.

A little calculus --- integrals

To integrate a function do almost the same, using the integral sign $\int$ instead of $\dfrac{d}{dx}$ for derivatives. Thus, write

for indefinite or definite integrals. The limits of integration are inserted using the subscript and superscript modes.

Example
Find $\int x^{3}\,dx$ and Just type the math (in Math mode) and choose the Evaluate button. Thus we have

$\$ Try the same thing using the Evaluate Numerically button. Note the different answers. Are they what you would expect.

Exercise
Compute the following integrals. If the Evaluate button doesn't work try the Evaluate Numerically button.
Yes, you can even do double integrals. Problem 5 gives two quite different answers depending on whether you choose Evaluate or Evaluate Numerically

Three shortcuts. To enter the following use the control key plus the one shown.

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Defining Generic Functions

You can use Define button to define a function. In Math mode type your function Place the insertion point anywhere in the function and choose the Define button. SNB has now memorized this function and you can do many things with it.
1. Evaluate. For example type and with the insertion point in the expression choose the Evaluate button. If you want actual numbers, choose the Evaluate Numerically button. We get
2. Differentiate. For example type and choose the Evaluate button. Alternatively try to compute the fourth derivative. We get and
3. Tangent line. Find the tangent line at the point We write and with the insertion point on the right side of the expression, choose the Evaluate button. We get
4. Integrals: Try this Place the insertion point on the right side of the expression, choose the Evaluate button. We get You can also do indefinite integrals
5. Composite functions. Define the function Now compose and to get $\ \$ Place the insertion point on the right side of the expression, choose the Evaluate button. We get Or for

Exercise

Define the functions and Do the following examples;

1. Find the tangent line to $f\left( t\right)$ at
2. Find
3. Find
4. Determine (Try both evaluate buttons.)
5. How would you find
Alternatively, you can also use Define + New Definition in the Maple menu to declare an expression of the form to be a function without specifying any of the function values or behavior. Thus you can use the function name as input when defining other functions or performing various operations on the function.

Define + New Definition

$g(x)=x^{2}-3x$

Evaluate

The Define + New Definition in the Maple menu shows many more options, such as Clear Definition, which can be handy to have.

Defining Generic Constants

You can use Define + New Definition to declare any valid expression name to be a constant. Scientific Notebook will then ignore such names when identifying dependent and independent variables.

Making tables and matrices.

If you need to make a table use the Table button You will obtain Table dialogue box and will need to input how many rows and columns you want. You can even decide on alignment of items within the cells.

Make your selections and click OK. To enter items, text, math, or graphics in the box, select the desired cell and type as usual. Cells of a table are in Text Mode by default.

Example

Make a table on a displayed line. Line the boxes. First select the Display button. Then choose the Table button.
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To line the boxes choose the table you've just made and choose Edit+Properties+Lines. Choose the Single button and the All button.

If you need to make a matrix use the Matrix button You will need to decide how many rows and columns you want. Make the selection and click OK. To enter items, text, math, or graphics in the box, select the desired cell and type as usual. Cells of a matrix are in default Math mode. \lbrack To make parentheses press ctrl+( , as described below.\rbrack

Example
Make a matrix on a displayed line. First select the Display button. Then choose the Matrix button Enter the numbers 1 through 12 in the cells. You can create the brackets after creating the matrix by choosing the matrix and pressing ctrl+(. Alternatively, you can press ctrl+(, place the insertion point inside the parentheses, and then choose the Matrix button.

You can also use large square brackets. Choose what you wanted bracketed. Click the Bracket button , or from the Insert menu, choose Brackets. Select the left and right brackets you wish. Here are two examples: square brackets and norm bars.

Example
With matrices you can perform the usual matrix operations.
1. Multiplication: Use the Evaluate button.
2. Addition Use the Evaluate button.
3. Scalar Multiplication: Use the Evaluate button.
4. Inverse: Use the Evaluate button.
There are many, many more matrix options. Peruse the options in the Maple+Matrices selection.

Typing Cases

Typing an expression using cases is a little tricky. A cases-type expression is of this form:

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The right side of the expression is a matrix surrounded by brackets. The right bracket is an empty bracket.

To enter an empty left or right bracket

Click the Bracket button , or from the File menu, choose Brackets.
If you want an empty left bracket, locate the empty bracket in the top row of brackets.
If you want an empty right bracket, locate the empty bracket in the bottom row of brackets.
Complete the bracket pair.
Choose OK.

To enter a case expression

Enter the expression to the left of the =.
Enter the =.
Create a matrix.
Enclose the matrix in brackets with an empty right bracket. The empty bracket is shown in the Brackets dialog box as .
Enter the case expression in the matrix.

To align the case expression

Edit the properties of the matrix.

Using the help menus

We have only touched on the thousands of features of Scientific Notebook. The help menus contain much more information than you can absorb in any reasonable time. Go to Help+Search or Help+Index+... Learn to use and depend on them. You can also find a great reference library on calculus, physics, and chemistry. Go to Help+Contents+Reference Library.