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\begin{document}


\begin{center}
{\Large Scientific Notebook Tutorial}
\end{center}

Scientific Notebook is a combination scientific/math word processor with a
symbolic engine (supplied by Maple) attached. Thus, one can both display and
do mathematical operations in Scientific Notebook.

\vspace{1pt}

\vspace{1pt}The entry and execution of mathematical operations is easier if
the Standard, Math Templates, Compute and Math Objects toolbars are
available. To add a toolbar use the menu sequence View/Toolbars and click on
the checkboxes of the desired menus. When you have finished selecting
toolbars, press the Close button.

\ 

There are two entry modes, text and math. If the menu button \textbf{T} \ is
displayed, you are in text mode. If the $M$ is displayed, you are in math
mode. To display or manipulate mathematical objects, you need to be in $M$%
ath mode. Unlike Maple, you are not required to enter multiplication between
variables! Stated differently, Scientific Notebook ''understands'' algebraic
notation. Exponents can be entered using the N$^{x}$ button, fractions by
using the $\frac {} {}$ button, parentheses by using the $\left( {}\right) $
button, radicals using the $\sqrt{}$ button. To enter absolute values $%
\left| {}\right| $ , type Crtl \TEXTsymbol{\vert} . Here \TEXTsymbol{\vert}
is the vertical line key on the upper right of a standard keyboard. As on
most calculators, use parentheses for grouping symbols, ''nesting'' them if
necessary to evaluate expressions stated in standard mathematical notation
with \lbrack\ \rbrack\ or \{ \} .

\vspace{1pt}

To algebraically simplify a mathematical expression, place the cursor in the
expression and press the Simplify button marked x$+$x=2x . To solve a single
equation for a variable, place the cursor in the equation and press the
Solve Exact button marked x ? . \ To solve a system of linear equations
enter the equations in an $n\times 1$ matrix (use the command sequence
Insert/Matrix) , with one equation to a row. When you have the same number
of unknowns as equations, put the cursor anywhere in the system, and then
press the Solve Exact button. This is shown below

\vspace{1pt}

$ 
\begin{array}{l}
3x+5y=1 \\ 
7x-5y=19%
\end{array}
$, Solution is : $\left\{ y=-1,x=2\right\} $

\vspace{1pt}

To verify this process, change one or both of the equations in the box
above. Then position the cursor in the box and press the solve exact (x ?)
button. The ''new'' solution should then be displayed.

\vspace{1pt}

To substitute for a variable, type an equation assigning a value or formula
for the variable, place the cursor in this equation, and then press the 
\textsf{New Definition} button marked f$($x$)$= . To ''free up'' a variable
so defined and thus ''restore'' its status as a free variable, highlight the
variable, and use the command sequence Maple/Define/Undefine .

\vspace{1pt}

To graph $y$ as a function of $x$, type the equation for $y$ in terms of $x$%
, place the cursor in this equation, and press the 2-D graph button. To
graph $z$ as a function of $x$ and $y$, follow a similar procedure, but use
the 3-D graph button next to the 2-D graph button.

\vspace{1pt}

To define $y=f(x)$ , i.e., $y$ as a function of $x$ for example to define
the function

$f$ whose value at $x$ is $ax^{2}+bx+c$

1.\qquad Enter the equation $f\left( x\right) =ax^{2}+bx+c$.

2.\qquad Place the insertion point in the equation.

3\qquad Click the \textsf{New Definition} button marked f$($x$)$= on the 
\textsf{Compute} toolbar or, from the \textsf{Define }submenu, choose 
\textsf{New Definition}.

Now the symbol $f$ represents the defined function and it behaves like a
function. For example, apply \textsf{Evaluate} to $f(t)$ to get $%
f(t)=at^{2}+bt+c$ and apply \textsf{Evaluate} to $f^{\prime }(t)$ to get $%
f^{\prime }(t)=2at+b$. Alternatively, to evaluate the derivative of $f(t),$
use the fraction key $\frac {} {}$ to enter

$\frac{d}{dt}f(t)=\allowbreak 2at+b$ and use the simplify or evaluate button
to display the answer.

\vspace{1pt}

Alternatively, we could evaluate the derivative from its definition as a
limit :

\vspace{1pt}

To find a limit of the form $\lim_{x\rightarrow a}g(x)$

1.\qquad Type \QTR{UserInput}{lim} while in mathematics mode.

2.\qquad Click the subscribt button \textbf{N}$_{x}$ and enter $x\rightarrow
a$ as a subscript.

3.\qquad Enter $g(x)$.

4.\qquad Choose \textsf{Evaluate}, the button marked \textsl{=?} .

\vspace{1pt}

For the above example

$\lim_{h\rightarrow 0}\frac{f(t+h)-f(t)}{h}=\allowbreak 2at+b$

\vspace{1pt}Infinite limits can also be done as in $\lim_{x\rightarrow
\infty }\frac{\sqrt{x^{2}+5x-2}}{x}=\allowbreak 1$

To illustrate the use of the chain rule, use the \textsf{New Definition}
button marked f$($x$)$= to define

$z=\frac{\sin (\pi x)}{x}$ \ followed by the function definition \ \ $%
f(t)=3t^{2}-6t+9$ . Now, contrast the following evaluations :

\vspace{1pt}

$f^{\prime }(x)=\allowbreak 6x-6$

$f^{\prime }(3y)=\allowbreak 18y-6$

\vspace{1pt}$\frac{d}{dt}f(t)=\allowbreak 6t-6$

$\frac{d}{dx}f(z)=\allowbreak -6\frac{-\left( \sin \pi x\cos \pi x\right)
\pi x+1-\cos ^{2}\pi x+\left( \cos \pi x\right) \pi x^{2}-\left( \sin \pi
x\right) x}{x^{3}}\allowbreak $

$f^{\prime }(z)\cdot \frac{d}{dx}z=\allowbreak \left( 6\frac{\sin \pi x}{x}%
-6\right) \frac{\left( \cos \pi x\right) \pi x-\sin \pi x}{x^{2}}%
=\allowbreak -6\frac{-\left( \sin \pi x\cos \pi x\right) \pi x+1-\cos
^{2}\pi x+\left( \cos \pi x\right) \pi x^{2}-\left( \sin \pi x\right) x}{%
x^{3}}\allowbreak $, where the simplify button was used to show the
equivalence of the last two calculations.

\vspace{1pt}

\vspace{1pt} To enter a definite integral

1.\qquad Click the integral button $\int $ or choose \textsf{Insert +
Operator} and choose the integral sign.

2.\qquad Click the subscribt button \textbf{N}$_{x}$ or choose \textsf{%
Insert + Subscript}.

3.\qquad Use the tab key to enter the upper limit of integration. (Limits of
integration work the same as any other subscripts or superscripts.)

4.\qquad Press the spacebar or the right arrow to get out of the
superscript, and type the rest of the expression Note : the differential
such as $dx$ is optional. It will be assumed if not entered explicitly.

5.\qquad Choose \textsf{Evaluate}, the button marked \textsl{=?} for an
analytic result or \textsf{Evaluate Numerically}, the button marked \textsl{=%
}$^{\#}$\textsl{? \ }for a numerical result.

\vspace{1pt}

For example :\qquad\ $\int_{0}^{\pi }(\sin (2x))^{2}dx=\allowbreak \frac{1}{2%
}\pi $

\vspace{1pt}\qquad \qquad \qquad \qquad \qquad $\int_{0}^{\infty
}e^{-x}(x^{4}+7x^{3}-3x^{2}+5x-11)dx=\allowbreak 54$

\vspace{1pt}

\qquad \qquad \qquad \qquad \qquad $\int_{0}^{\infty }\frac{\sin (x)}{x}%
dx=\allowbreak \frac{1}{2}\pi $

\vspace{1pt}

\qquad \qquad \qquad \qquad \qquad $\int_{0}^{\infty }\frac{\sin (x)}{\sqrt{%
x^{2}+1}}dx=\allowbreak \int_{0}^{\infty }\frac{\sin x}{\sqrt{\left(
x^{2}+1\right) }}\,dx=\allowbreak .\,\allowbreak 873\,084\,242\,\allowbreak
650\,867\,539\,\allowbreak 074\,84\allowbreak $

In this last example, \textsf{Evaluate} returned the original integral,
meaning Scientific Notebook was unable to find an analytic answer. The
second answer is from \textsf{Evaluate Numerically.}

Standard mathematical functions like the $\sin $ can either be typed in $M$
mode or be entered using the command sequence Insert/Math Name. \vspace{1pt}%
The Scientific Notebook Help menu is \textbf{helpful. Make use of it!}

\vspace{1pt}

The following commands perform the same calculations as in the Derive and
Maple notes:

\vspace{1pt}

$x^{2}-5x+6=\allowbreak \left( x-2\right) \left( x-3\right) $

$\allowbreak $use the command sequence Maple/Factor

$x^{2}+7x-11$, Solution is : $\left\{ x=-\frac{7}{2}+\frac{1}{2}\sqrt{93}%
\right\} ,\left\{ x=-\frac{7}{2}-\frac{1}{2}\sqrt{93}\right\} $

$\int \frac{1}{1+x^{2}}=\allowbreak \arctan x$

$\left( x+5\right) ^{4}=\allowbreak x^{4}+20x^{3}+150x^{2}+500x+625$

use the Expand button (a red ''ballon''?) or the command sequence
Maple/Expand

\vspace{1pt}

$f:=x-\cos (x)$\FRAME{itbpF}{3in}{2in}{0in}{}{}{}{\special{language
"Scientific Word";type "MAPLEPLOT";width 3in;height 2in;depth 0in;display
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To increase the number of digits in a numerical computation use the command
sequence Maple/Settings and increase Digits Used in Computations and Digits
Used in Display.

$f=0$, Solution is : $\left\{ x=.\,\allowbreak 739\,085\,133\,\allowbreak
215\,160\,641\,\allowbreak 655\,312\,1\right\} \allowbreak $,

\vspace{1pt}

$x^{2}-y^{2}$\FRAME{itbpF}{5.1353in}{3.4238in}{0.0311in}{}{}{}{%
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\end{document}
