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%TCIDATA{<META NAME="Title" CONTENT="Plotting">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Wed May 14 11:49:08 1997}
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\input{tcilatex}
\begin{document}


\subsection{Plotting\label{Plotting}\hrulefill}

In \textit{Scientific Notebook,} you can create 2-dimensional and
3-dimensional plots of polynomials, trigonometric functions, and
exponentials.

\subparagraph{\FRAME{itbpF}{50.75pt}{21.75pt}{6pt}{}{}{ex3.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 50.75pt;height 21.75pt;depth 6pt;original-width
48.875pt;original-height 19.5625pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'ex3.WMF';file-properties "XNPEU";}}Plot $x^{2}$}

\begin{enumerate}
\item  Click\FRAME{itbpF}{20.125pt}{20.125pt}{2pt}{}{}{text.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 20.125pt;height 20.125pt;depth
2pt;original-width 16.0625pt;original-height 16.0625pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'text.wmf';file-properties
"XNPEU";}}or, from the Insert menu, choose Math; then type \textbf{x }, click%
\FRAME{itbpF}{19.5625pt}{18.8125pt}{2pt}{}{}{supscrip.wmf}{\special{language
"Scientific Word";type "GRAPHIC";display "PICT";valid_file "F";width
19.5625pt;height 18.8125pt;depth 2pt;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'supscrip.wmf';file-properties "XNPEU";}}or,
from the Insert menu, choose Superscript; then type \textbf{2} and press
spacebar.

\item  From the Maple menu, choose Plot 2D and then choose Rectangular.
Maple plots the expression: 
\[
x^{2}\FRAME{itbpF}{3in}{2.0003in}{0in}{}{}{}{\special{language "Scientific
Word";type "MAPLEPLOT";width 3in;height 2.0003in;depth 0in;display
"FULL";function \TEXUX{$x^{2}$};linecolor "black";linestyle 1;linethickness
1;pointstyle "point";xmin "-5";xmax "5";xviewmin "-5.000000";xviewmax
"5.000000";yviewmin "-0.499975";yviewmax "25.510000";phi 45;theta
45;plottype 4;numpoints 49;axesstyle "normal";xis \TEXUX{x};var1name
\TEXUX{$x$};}}
\]

Add to the plot:

\begin{enumerate}
\item  Press Enter to start a new line and then start mathematics.

\item  Type \textbf{x}, click\FRAME{itbpF}{19.5625pt}{18.8125pt}{2pt}{}{}{%
supscrip.wmf}{\special{language "Scientific Word";type "GRAPHIC";display
"PICT";valid_file "F";width 19.5625pt;height 18.8125pt;depth
2pt;original-width 17.8125pt;original-height 16.9375pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'supscrip.wmf';file-properties
"XNPEU";}}, and type \textbf{3}.

\item  Select the expression and drag it onto the plot. Maple replots,
adding the new value: \medskip 
\[
x^{2}\FRAME{itbpF}{3in}{2.0003in}{0in}{}{}{}{\special{language "Scientific
Word";type "MAPLEPLOT";width 3in;height 2.0003in;depth 0in;display
"FULL";function \TEXUX{$x^{2}$};linecolor "black";linestyle 1;linethickness
1;pointstyle "point";function \TEXUX{$x^{3}$};linecolor "black";linestyle
1;linethickness 1;pointstyle "point";xmin "-5";xmax "5";xviewmin
"-5.000000";xviewmax "5.000000";yviewmin "-130.000000";yviewmax
"130.100000";phi 45;theta 45;plottype 4;numpoints 49;axesstyle "normal";xis
\TEXUX{x};var1name \TEXUX{$x$};}}
\]
\end{enumerate}
\end{enumerate}

\subparagraph{\FRAME{itbpF}{50.75pt}{21.75pt}{6pt}{}{}{ex3.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid-file
"F";width 50.75pt;height 21.75pt;depth 6pt;original-width
48.875pt;original-height 19.5625pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'ex3.WMF';file-properties "XNPEU";}}Plot \texttt{%
\ sin}\textit{\texttt{\textit{\thinspace }}}$2t$}

\begin{enumerate}
\item  Click\FRAME{itbpF}{20.125pt}{20.125pt}{2pt}{}{}{text.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 20.125pt;height 20.125pt;depth
2pt;original-width 16.0625pt;original-height 16.0625pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'text.wmf';file-properties
"XNPEU";}}or, from the Insert menu, choose Math to start mathematics; then
type \textbf{sin2t}.

\item  From the Maple menu, choose Plot 2D and then choose Polar. Maple
plots the expression:\ \medskip 
\[
\sin 2t\FRAME{itbpF}{3in}{2.0003in}{0in}{}{}{}{\special{language "Scientific
Word";type "MAPLEPLOT";width 3in;height 2.0003in;depth 0in;display
"FULL";function \TEXUX{$\sin 2t$};linecolor "black";linestyle
1;linethickness 1;pointstyle "point";xmin "-3.1416";xmax "3.1416";xviewmin
"-0.7993";xviewmax "0.7997";yviewmin "-0.7992";yviewmax "0.7995";recompute
TRUE;phi 45;theta 45;plottype 8;numpoints 49;axesstyle "normal";xis
\TEXUX{t};var1name \TEXUX{$\theta $};}}
\]
\end{enumerate}

\subparagraph{\FRAME{itbpF}{50.75pt}{21.75pt}{6pt}{}{}{ex3.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid-file
"F";width 50.75pt;height 21.75pt;depth 6pt;original-width
48.875pt;original-height 19.5625pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'ex3.WMF';file-properties "XNPEU";}}Plot $%
x^{2}y^{3}$}

\begin{enumerate}
\item  Click\FRAME{itbpF}{20.125pt}{20.125pt}{2pt}{}{}{text.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 20.125pt;height 20.125pt;depth
2pt;original-width 16.0625pt;original-height 16.0625pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'text.wmf';file-properties
"XNPEU";}}or, from the Insert menu, choose Math to start mathematics.

\item  Type \textbf{x}, click\FRAME{itbpF}{19.5625pt}{18.8125pt}{2pt}{}{}{%
supscrip.wmf}{\special{language "Scientific Word";type "GRAPHIC";display
"PICT";valid_file "F";width 19.5625pt;height 18.8125pt;depth
2pt;original-width 17.8125pt;original-height 16.9375pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'supscrip.wmf';file-properties
"XNPEU";}}, type \textbf{2}, and press spacebar; then type \textbf{y}, click%
\FRAME{itbpF}{19.5625pt}{18.8125pt}{2pt}{}{}{supscrip.wmf}{\special{language
"Scientific Word";type "GRAPHIC";display "PICT";valid_file "F";width
19.5625pt;height 18.8125pt;depth 2pt;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'supscrip.wmf';file-properties "XNPEU";}}, and
type \textbf{3}.

\item  From the Maple menu, choose Plot 3D and then choose Rectangular.
Maple plots the expression: \ \medskip 
\[
x^{2}y^{3}\FRAME{itbpF}{3in}{2.0003in}{0in}{}{}{}{\special{language
"Scientific Word";type "MAPLEPLOT";width 3in;height 2.0003in;depth
0in;display "FULL";function \TEXUX{$x^{2}y^{3}$};linecolor "black";linestyle
1;linethickness 1;pointstyle "point";xmin "-5";xmax "5";ymin "-5";ymax
"5";xviewmin "-5.2";xviewmax "5.204";yviewmin "-5.2";yviewmax
"5.204";zviewmin "-3250";zviewmax "3253";phi 45;theta 45;plottype
5;num-x-gridlines 25;num-y-gridlines 25;plotstyle "wireframe";axesstyle
"none";plotshading "Z";xis \TEXUX{x};yis \TEXUX{y};var1name
\TEXUX{$x$};var2name \TEXUX{$y$};}} 
\]
\end{enumerate}

\subparagraph{\FRAME{itbpF}{50.75pt}{21.75pt}{6pt}{}{}{ex3.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid-file
"F";width 50.75pt;height 21.75pt;depth 6pt;original-width
48.875pt;original-height 19.5625pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'ex3.WMF';file-properties "XNPEU";}}Plot $\left[
x\mathit{\mathtt{\mathit{\,}}}\text{\texttt{sin}}\mathit{\mathtt{\mathit{\,}}%
}x\mathit{\mathtt{\mathit{\,}}}\text{\texttt{cos}}\mathit{\mathtt{\mathit{\,}%
}}y,x\text{\textit{\texttt{\textit{\thinspace }}}\texttt{cos}}\mathit{%
\mathtt{\mathit{\,}}}x\mathit{\mathtt{\mathit{\,}}}\text{\textit{\texttt{%
cos\thinspace }}}y,x\text{\thinspace \texttt{sin\thinspace }}y\right] $}

\noindent Remember that \textit{Scientific Notebook} understands
trigonometric functions and spaces your mathematics correctly.

\begin{enumerate}
\item  Click\FRAME{itbpF}{22.4375pt}{21.0625pt}{2pt}{}{}{sqbrack.wmf}{%
\special{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 22.4375pt;height 21.0625pt;depth 2pt;original-width
20.3125pt;original-height 18.8125pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'Sqbrack.wmf';file-properties "XNPEU";}}.

\item  Type \textbf{xsinxcosy, }

\item  Type \textbf{xcosxcosy,}

\item  Type \textbf{xsiny}.

\item  From the Maple menu, choose Plot 3D and then choose Rectangular.
Maple produces a plot whose components you can change.

\item  Click\FRAME{itbpF}{19.5625pt}{18.8125pt}{2pt}{}{}{property.wmf}{%
\special{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 19.5625pt;height 18.8125pt;depth 2pt;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'property.wmf';file-properties "XNPEU";}}and
select the Plot Components tab.

\item  In the Domain Intervals area, set $0<x<6.28$ and set $0<y<3.14.$
\end{enumerate}

In the Plot Style area, select WireFrame, and choose OK. Maple replots the
expression: \ \medskip 
\[
\left[ x\sin x\cos y,x\cos x\cos y,x\sin y\right] \FRAME{itbpF}{3in}{2.0003in%
}{0in}{}{}{}{\special{language "Scientific Word";type "MAPLEPLOT";width
3in;height 2.0003in;depth 0in;display "FULL";function \TEXUX{$\left[ x\sin
x\cos y,x\cos x\cos y,x\sin y\right] $};linecolor "black";linestyle
1;linethickness 1;pointstyle "point";xmin "0";xmax "6.28";ymin "0";ymax
"3.14";xviewmin "0";xviewmax "6.28";yviewmin "0";yviewmax "3.14";zviewmin
"-0.1256";zviewmax "6.408";rangeset"XY";phi 45;theta 45;plottype
5;num-x-gridlines 25;num-y-gridlines 25;plotstyle "wireframe";axesstyle
"none";plotshading "Z";xis \TEXUX{x};yis \TEXUX{y};var1name
\TEXUX{$x$};var2name \TEXUX{$y$};}} 
\]

\subparagraph{Plot these expressions\label{exercises}}

\begin{quotation}
\rule[-0.05in]{0in}{0.3in}\qquad Plot 2D, Rectangular: $x\sin \dfrac{1}{x}%
\vspace{0.1in}$

\qquad Plot 2D, Parametric: $\left( \sin 2t,\cos 3t\right) \vspace{0.1in}$

\qquad Plot 2D, Implicit: $\left( x-2\right) ^{2}+\left( y-3\right) ^{2}=25$%
, where $-3\leq x\leq 7$ and $-2\leq y\leq 8\vspace{0.1in}$

\qquad Plot 3D, Cylindrical: $1-z$, where $0\leq \theta \leq 2\pi $ and $%
0\leq z\leq 1\vspace{0.1in}$

\qquad Plot 3D, Spherical: $2$, where $0\leq \theta \leq 2\pi $ and 0$\leq
z\leq 2\pi $
\end{quotation}

\end{document}
