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psfig is now includegraphics
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kisonecat committed May 17, 2022
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Expand Up @@ -101,7 +101,7 @@ \subsubsection*{Drawing Contours Using \Matlab}

\begin{figure}[htb]
\centerline{%
\psfig{file=../figures/contour1.eps,width=3.5in}}
\includegraphics[width=3.5in]{../figures/contour1.pdf}}
\caption{Contour lines of $F(t,x)=x^2-xt+t$ for
$(t,x)\in[-1.5,1.5]\times[-1.5,1.5]$.}
\label{Fig:contour1}
Expand Down Expand Up @@ -142,7 +142,7 @@ \subsubsection*{Drawing Contours Using \Matlab}

\begin{figure}[htb]
\centerline{%
\psfig{file=../figures/contour2.eps,width=3.7in}}
\includegraphics[width=3.7in]{../figures/contour2.pdf}}
\caption{The solution of \protect\eqref{eq:exactex1} for the
initial value $(t_0,x_0)=(-0.5,-1)$ computed by {\dfield}.}
\label{Fig:contour2}
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\begin{figure}[htb]
\centerline{%
\psfig{file=../figures/contour3.eps,width=3.5in}}
\includegraphics[width=3.5in]{../figures/contour3.pdf}}
\caption{Solutions of the differential equation
\protect\eqref{eq:exacex2}
corresponding to the levels $c=0,3,6,9,12$ in the rectangle
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Expand Up @@ -34,7 +34,7 @@
The result is given in Figure~\ref{c14.6.8}.
\begin{figure}[htb]
\centerline{%
\psfig{file=exfigure/fig17-6-9.eps,width=3.0in}}
\includegraphics[width=3.0in]{exfigure/fig17-6-9.pdf}}
\exercap{c14.6.8}
\end{figure}

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8 changes: 4 additions & 4 deletions additionalTechniquesForSolvingODEs/hamiltonianSystems.tex
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Expand Up @@ -134,7 +134,7 @@ \subsection*{Potential Systems}
the existence of two homoclinic trajectories\index{trajectory!homoclinic}.
\begin{figure}[htb]
\centerline{%
\psfig{file=../figures/ham.eps,width=3.5in}}
\includegraphics[width=3.5in]{../figures/ham.pdf}}
\caption{Phase portrait of \protect\eqref{e:hamex1}}
\label{F:hamex}
\end{figure}
Expand Down Expand Up @@ -184,14 +184,14 @@ \subsection*{Newton's Second Law and Potential Systems}
\end{itemize}
\begin{figure}[htb]
\centerline{%
\psfig{file=../figures/pendulum.eps,width=2.0in}}
\includegraphics[width=2.0in]{../figures/pendulum.pdf}}
\caption{Pendulum geometry}
\label{F:pendulum}
\end{figure}
The phase portrait for the pendulum equations is shown in Figure~\ref{F:ppen}.
\begin{figure}[htb]
\centerline{%
\psfig{file=../figures/ppen.eps,width=3.5in}}
\includegraphics[width=3.5in]{../figures/ppen.pdf}}
\caption{Phase portrait of the pendulum equation
\protect\eqref{e:pendulum}}
\label{F:ppen}
Expand Down Expand Up @@ -233,7 +233,7 @@ \subsubsection*{The Two Body Problem}

\begin{figure}[htb]
\centerline{%
\psfig{file=../figures/tbp.eps,height=2.5in}}
\includegraphics[height=2.5in]{../figures/tbp.pdf}}
\caption{Phase portrait of the equation
\protect\eqref{e:tbp}}
\label{fig:tbp}
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Expand Up @@ -27,7 +27,7 @@

\begin{figure}[htb]
\centerline{%
\psfig{file=exfigure/fig14-7-10.eps,width=3.0in}}
\includegraphics[width=3.0in]{exfigure/fig14-7-10.pdf}}
\exercap{c14.7.10}
\end{figure}

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Expand Up @@ -36,7 +36,7 @@

\begin{figure}[htb]
\centerline{%
\psfig{file=exfigure/fig14-7-11.eps,width=3.0in}}
\includegraphics[width=3.0in]{exfigure/fig14-7-11.pdf}}
\exercap{c14.7.11}
\end{figure}

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4 changes: 2 additions & 2 deletions additionalTechniquesForSolvingODEs/higherOrderEquations.tex
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Expand Up @@ -206,8 +206,8 @@ \subsubsection*{An Example of an Electrical Circuit}
The result of this computation is shown in Figure~\ref{Fig:micro1}.
\begin{figure*}[htb]
\centerline{%
\psfig{file=../figures/microx1.eps,width=3.0in}
\psfig{file=../figures/microx2.eps,width=3.0in}}
\includegraphics[width=3.0in]{../figures/microx1.pdf}
\includegraphics[width=3.0in]{../figures/microx2.pdf}}
\caption{The two components of the solution of
\protect\eqref{E:RCLM} for $t\in[0,30]$ with initial
condition $X(0)=(1,1)^t$.}
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Expand Up @@ -39,7 +39,7 @@
result is displayed in Figure~\ref{c14.3.7a}.
\begin{figure}[htb]
\centerline{%
\psfig{file=exfigure/fig17-4-6.eps,width=3.0in}}
\includegraphics[width=3.0in]{exfigure/fig17-4-6.pdf}}
\exercap{c14.3.7a}
\end{figure}

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result is displayed in Figure~\ref{c14.3.7b}.
\begin{figure}[htb]
\centerline{%
\psfig{file=exfigure/fig17-4-7.eps,width=3.0in}}
\includegraphics[width=3.0in]{exfigure/fig17-4-7.pdf}}
\exercap{c14.3.7b}
\end{figure}

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result is displayed in Figure~\ref{c14.3.7c}.
\begin{figure}[htb]
\centerline{%
\psfig{file=exfigure/fig17-4-8.eps,width=3.0in}}
\includegraphics[width=3.0in]{exfigure/fig17-4-8.pdf}}
\exercap{c14.3.7c}
\end{figure}

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result is displayed in Figure~\ref{c14.3.7d}.
\begin{figure}[htb]
\centerline{%
\psfig{file=exfigure/fig17-4-9.eps,width=3.0in}}
\includegraphics[width=3.0in]{exfigure/fig17-4-9.pdf}}
\exercap{c14.3.7d}
\end{figure}

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Expand Up @@ -201,8 +201,8 @@ \subsubsection*{Two Examples of Variation of Parameters}

\begin{figure*}[htb]
\centerline{%
\psfig{file=../figures/solnm.eps,width=2.8in}
\psfig{file=../figures/solnd.eps,width=3.0in}}
\includegraphics[width=2.8in]{../figures/solnm.pdf}
\includegraphics[width=3.0in]{../figures/solnd.pdf}}
\caption{(Left) Graph of solution~\protect\eqref{e:solnth} to equation
\protect\eqref{e:solntheq}. (Right) The time series for solution to
\protect\eqref{e:solntheq} with initial condition $x(1)=0$ using
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Expand Up @@ -20,7 +20,7 @@

\begin{figure}[htb]
\centerline{%
\psfig{file=exfigure/fig17-1-11.eps,width=3.0in}}
\includegraphics[width=3.0in]{exfigure/fig17-1-11.pdf}}
\exercap{c14.2.11a}
\end{figure}
Using variation of parameters we find that the general solution to the
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\begin{figure}[htb]
\centerline{%
\psfig{file=exfigure/fig17-1-12.eps,width=3.0in}}
\includegraphics[width=3.0in]{exfigure/fig17-1-12.pdf}}
\exercap{c14.2.11b}
\end{figure}

Expand All @@ -76,7 +76,7 @@

\begin{figure}[htb]
\centerline{%
\psfig{file=exfigure/fig17-1-13.eps,width=3.0in}}
\includegraphics[width=3.0in]{exfigure/fig17-1-13.pdf}}
\exercap{c14.2.11c}
\end{figure}

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12 changes: 6 additions & 6 deletions autonomousPlanarNonlinearSystems/equilibriaAndLinearization.tex
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Expand Up @@ -111,8 +111,8 @@

\begin{figure*}[htb]
\centerline{%
\psfig{file=../figures/spirala.eps,width=3.5in}
\psfig{file=../figures/spiralb.eps,width=3.0in}}
\includegraphics[width=3.5in]{../figures/spirala.pdf}
\includegraphics[width=3.0in]{../figures/spiralb.pdf}}
\caption{(Left) Trajectory of \protect\eqref{e:linearizedeqn}
near the spiral sink $Z_2$. (Right) The time series $x$
versus $t$ for this solution.}
Expand Down Expand Up @@ -274,7 +274,7 @@ \subsubsection*{An Example with Analytically Solvable Equilibria}

\begin{figure}[htb]
\centerline{%
\psfig{file=../figures/ex12exam.eps,width=3.5in}}
\includegraphics[width=3.5in]{../figures/ex12exam.pdf}}
\caption{Equilibria and connections of \protect\eqref{e1:exer}.}
\label{F:ex12}
\end{figure}
Expand Down Expand Up @@ -315,16 +315,16 @@ \subsubsection*{An Example Where Equilibria are Not Analytically Solvable}

\begin{figure*}[htb]
\centerline{%
\psfig{file=../figures/saddlea.eps,width=3.2in}
\psfig{file=../figures/saddleb.eps,width=3.2in}}
\includegraphics[width=3.2in]{../figures/saddlea.pdf}
\includegraphics[width=3.2in]{../figures/saddleb.pdf}}
\caption{(Left) Direction field of \protect\eqref{e:gradexam}.
(Right) Phase plane with equilibria and stable orbits.}
\label{F:gradexam}
\end{figure*}

\begin{figure}[htb]
\centerline{%
\psfig{file=../figures/grad.eps,width=3.in}}
\includegraphics[width=3.in]{../figures/grad.pdf}}
\caption{Stylized phase plane portrait of \protect\eqref{e:gradexam}.}
\label{F:gradexamstyle}
\end{figure}
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Expand Up @@ -36,8 +36,8 @@

\begin{figure}[htb]
\centerline{%
\psfig{file=exfigure/8-2-1a.eps,width=2.75in}
\psfig{file=exfigure/8-2-1b.eps,width=2.75in}}
\includegraphics[width=2.75in]{exfigure/8-2-1a.pdf}
\includegraphics[width=2.75in]{exfigure/8-2-1b.pdf}}
\exercaptwo{c8.2.1}
\end{figure}

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Expand Up @@ -49,7 +49,7 @@

\begin{figure}[htb]
\centerline{%
\psfig{file=exfigure/8-2-5.eps,width=3.0in}}
\includegraphics[width=3.0in]{exfigure/8-2-5.pdf}}
\exercap{c8.2.5}
\end{figure}

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Expand Up @@ -64,7 +64,7 @@

\begin{figure}[htb]
\centerline{%
\psfig{file=exfigure/8-2-7.eps,width=3.0in}}
\includegraphics[width=3.0in]{exfigure/8-2-7.pdf}}
\exercap{c8.2.7}
\end{figure}

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Expand Up @@ -19,8 +19,8 @@

\begin{figure}[htb]
\centerline{%
\psfig{file=exfigure/8-2-10a.eps,width=2.75in}
\psfig{file=exfigure/8-2-10b.eps,width=2.75in}}
\includegraphics[width=2.75in]{exfigure/8-2-10a.pdf}
\includegraphics[width=2.75in]{exfigure/8-2-10b.pdf}}
\exercaptwo{c8.2.10}
\end{figure}

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Expand Up @@ -22,7 +22,7 @@

\begin{figure}[htb]
\centerline{%
\psfig{file=exfigure/8-2-12.eps,width=3.0in}}
\includegraphics[width=3.0in]{exfigure/8-2-12.pdf}}
\exercap{c8.2.12}
\end{figure}

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18 changes: 9 additions & 9 deletions autonomousPlanarNonlinearSystems/introduction.tex
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Expand Up @@ -45,7 +45,7 @@

\begin{figure}[htb]
\centerline{%
\psfig{file=../figures/pp1d.eps,height=0.6in}}
\includegraphics[height=0.6in]{../figures/pp1d.pdf}}
\caption{Phase line plot for the one dimensional equation
\protect\eqref{e:1dexample}.}
\label{F:pp1d}
Expand All @@ -68,7 +68,7 @@

\begin{figure}[htb]
\centerline{%
\psfig{file=../figures/pp1dt.eps,height=2.0in}}
\includegraphics[height=2.0in]{../figures/pp1dt.pdf}}
\caption{Time series for solution to \protect\eqref{e:1dexample}
with initial condition between $0$ and $1$.}
\label{F:pp1dt}
Expand Down Expand Up @@ -171,8 +171,8 @@ \subsubsection*{A Linear Equation}

\begin{figure*}[htb]
\centerline{%
\psfig{file=../figures/locala.eps,height=1.8in}
\psfig{file=../figures/localb.eps,height=2.0in}}
\includegraphics[height=1.8in]{../figures/locala.pdf}
\includegraphics[height=2.0in]{../figures/localb.pdf}}
\caption{(Left) Sketch of phase plane of \protect\eqref{e:localexam}
based on eigenvalues and eigenvectors of $C$. (Right) Trajectories
of \protect\eqref{e:localexam} using {\pplane}.}
Expand Down Expand Up @@ -202,7 +202,7 @@ \subsubsection*{The Addition of Nonlinear Terms}
Figure~\ref{F:local} (right).
\begin{figure}[hbt]
\centerline{%
\psfig{file=../figures/globala.eps,height=2.0in}}
\includegraphics[height=2.0in]{../figures/globala.pdf}}
\caption{Trajectories of \protect\eqref{e:globalexam}
on the square $-0.5\leq x,y \leq 0.5$ using {\pplane}.}
\label{F:globala}
Expand All @@ -226,8 +226,8 @@ \subsubsection*{The Addition of Nonlinear Terms}
system. See Figure~\ref{F:globalb} (left).
\begin{figure*}[htb]
\centerline{%
\psfig{file=../figures/globalb.eps,height=2.0in}
\psfig{file=../figures/globalc.eps,height=2.0in}}
\includegraphics[height=2.0in]{../figures/globalb.pdf}
\includegraphics[height=2.0in]{../figures/globalc.pdf}}
\caption{(Left) Trajectories of \protect\eqref{e:globalexam}
on the square $-5\leq x,y \leq 5$ using {\pplane}. (Right) A
phase plane portrait of this equation.}
Expand Down Expand Up @@ -260,8 +260,8 @@ \subsubsection*{The Importance of Phase Plane Portraits}

\begin{figure*}[htb]
\centerline{%
\psfig{file=../figures/nltraj.eps,height=2.5in}
\psfig{file=../figures/nlts.eps,height=2.0in}}
\includegraphics[height=2.5in]{../figures/nltraj.pdf}
\includegraphics[height=2.0in]{../figures/nlts.pdf}}
\caption{(Left) Trajectory of \protect\eqref{e:globalexam}
through $(-0.1,0.1)$. (Right) Time series $y$ versus $t$ of
this solution.}
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2 changes: 1 addition & 1 deletion autonomousPlanarNonlinearSystems/introduction/00200.tex
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Expand Up @@ -20,7 +20,7 @@

\begin{figure}[htb]
\centerline{%
\psfig{file=exfigure/8-1-1.eps,width=3.5in}}
\includegraphics[width=3.5in]{exfigure/8-1-1.pdf}}
\exercap{c8.1.1}
\end{figure}

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4 changes: 2 additions & 2 deletions autonomousPlanarNonlinearSystems/introduction/00300.tex
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Expand Up @@ -38,8 +38,8 @@

\begin{figure}[htb]
\centerline{%
\psfig{file=exfigure/8-1-2a.eps,width=2.75in}
\psfig{file=exfigure/8-1-2b.eps,width=2.75in}}
\includegraphics[width=2.75in]{exfigure/8-1-2a.pdf}
\includegraphics[width=2.75in]{exfigure/8-1-2b.pdf}}
\exercaptwo{c8.1.2}
\end{figure}

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6 changes: 3 additions & 3 deletions autonomousPlanarNonlinearSystems/introduction/00400.tex
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Expand Up @@ -47,9 +47,9 @@

\begin{figure}[htb]
\centerline{%
\psfig{file=exfigure/8-1-3a.eps,width=1.8in}
\psfig{file=exfigure/8-1-3b.eps,width=1.8in}
\psfig{file=exfigure/8-1-3c.eps,width=1.8in}}
\includegraphics[width=1.8in]{exfigure/8-1-3a.pdf}
\includegraphics[width=1.8in]{exfigure/8-1-3b.pdf}
\includegraphics[width=1.8in]{exfigure/8-1-3c.pdf}}
\centerline{Figure~\ref{c8.1.3a}\hspace{1.2in}
Figure~\ref{c8.1.3b}\hspace{1.2in}Figure~\ref{c8.1.3c}}
\end{figure}
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8 changes: 4 additions & 4 deletions autonomousPlanarNonlinearSystems/periodicSolutions.tex
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Expand Up @@ -77,8 +77,8 @@ \subsubsection*{Nonhyperbolic Centers}

\begin{figure*}[htb]
\centerline{%
\psfig{file=../figures/periodic.eps,width=3.5in}
\psfig{file=../figures/period2.eps,width=3.5in}}
\includegraphics[width=3.5in]{../figures/periodic.pdf}
\includegraphics[width=3.5in]{../figures/period2.pdf}}
\caption{(Left) Trajectories of \protect\eqref{e:planeper}
when $\tau=3$. (Right) A time series of one solution.}
\label{F:planarperiodic}
Expand Down Expand Up @@ -110,8 +110,8 @@ \subsubsection*{Nonhyperbolic Centers}

\begin{figure*}[htb]
\centerline{%
\psfig{file=../figures/period3.eps,width=3.5in}
\psfig{file=../figures/period4.eps,width=3.5in}}
\includegraphics[width=3.5in]{../figures/period3.pdf}
\includegraphics[width=3.5in]{../figures/period4.pdf}}
\caption{(Left) A trajectory of \protect\eqref{e:nonlincenter}
that spirals towards the origin. Note the slow convergence due to the fact
that the origin is not hyperbolic. (Right) A trajectory of
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