%% This document created by Scientific Notebook (R) Version 3.0


\documentclass[12pt,thmsa]{article}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{sw20jart}

%TCIDATA{TCIstyle=article/art4.lat,jart,sw20jart}

%TCIDATA{<META NAME="ViewSettings" CONTENT="23">}
%TCIDATA{<META NAME="GraphicsSave" CONTENT="32">}
%TCIDATA{<META NAME="Title" CONTENT="Reference/Mathematics/Ordinary Differential Equations">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Sun Mar 30 17:07:00 1997}
%TCIDATA{Language=American English}
%TCIDATA{CSTFile=Reference.cst}
%TCIDATA{PageSetup=72,72,72,72,0}
%TCIDATA{<LINK REL="contents" HREF="..\Reference\ReferenceIndex.tex#Reference Index">}
%TCIDATA{<LINK REL="next" HREF="ODE01_01.tex">}
%TCIDATA{<LINK REL="parent" HREF="Mathematics.tex">}
%TCIDATA{AllPages=
%F=36,\PARA{038<p type="texpara" tag="Body Text" >\hfill \thepage}
%}


\input{tcilatex}
\begin{document}


\section{Ordinary Differential Equations}

An \textbf{ordinary differential equation} expresses a relationship between
one or more derivatives of an unspecified function of a single variable.
Differential equations find application in subjects where one or more
quantities under study are to be determined from their known dynamic
behavior. \vspace{1pt}The changing nature of a quantity is frequently
formulated as a relationship between its derivatives.

\subsection{\ Contents}

\subsubsection{First Order Equations}

\begin{itemize}
\item[+]  \hyperref{Basic Theory of First-Order Equations}{}{}{ODE01_01.tex}

\item[+]  \hyperref{Separable and Homogeneous Equations}{}{}{ODE01_02.TEX}

\item[+]  \hyperref{Linear and Bernoulli Equations}{}{}{ODE01_03.TEX}

\item[+]  \hyperref{Exact Differential Equations}{}{}{ODE01_04.TEX}
\end{itemize}

\subsubsection{Linear Differential Equations}

\begin{itemize}
\item[+]  \hyperref{Basic Theory of Linear Differential Equations}{}{}{%
ODE02_01.tex}

\item[+]  \hyperref{Equations with Constant Coefficients}{}{}{ODE02_02.tex}

\item[+]  \hyperref{Cauchy-Euler Equation}{}{}{ODE02_03.tex}

\item[+]  \hyperref{Power-Series Solutions}{}{}{ODE02_04.tex}
\end{itemize}

\subsection{\protect\vspace{1pt}\ Related Reference Topics}

{\small \hyperref{Calculus}{}{}{CAL_contents.tex}}\hfill 

\subsection{\ Related Scientific Notebook Topics}

{\small \hyperref{Calculus}{}{}{../../Help/DM7.tex}}

{\small \hyperref{Differential Equations}{}{}{../../Help/DM10.tex}}

{\small \hyperref{Sample exercises with solutions}{}{}{%
../../Help/DM10-5.tex#Exercises}}\hfill 

\noindent \hrulefill

\begin{center}
\begin{tabular}{ccc}
{\small \hyperref{\FRAME{itbpF}{13.9375pt}{14.4375pt}{3pt}{}{}{nblogo.wmf}{%
\special{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid_file "F";width 13.9375pt;height 14.4375pt;depth
3pt;original-width 24.0625pt;original-height 24.8125pt;cropleft "0";croptop
"0.9959";cropright "0.9937";cropbottom "0";filename
'Nblogo.wmf';file-properties "XNPEU";}}Computing Techniques}{}{}{%
../../Help/DMindex.tex}} & {\small \hyperref{\FRAME{itbpF}{13.9375pt}{%
14.4375pt}{3pt}{}{}{nblogo.wmf}{\special{language "Scientific Word";type
"GRAPHIC";maintain-aspect-ratio TRUE;display "PICT";valid_file "F";width
13.9375pt;height 14.4375pt;depth 3pt;original-width
24.0625pt;original-height 24.8125pt;cropleft "0";croptop "0.9959";cropright
"0.9937";cropbottom "0";filename 'Nblogo.wmf';file-properties "XNPEU";}}%
General Information}{}{}{../../Help/Index.tex}} & {\small \hyperref{\FRAME{%
itbpF}{13.9375pt}{14.4375pt}{3pt}{}{}{nblogo.wmf}{\special{language
"Scientific Word";type "GRAPHIC";maintain-aspect-ratio TRUE;display
"PICT";valid_file "F";width 13.9375pt;height 14.4375pt;depth
3pt;original-width 24.0625pt;original-height 24.8125pt;cropleft "0";croptop
"0.9959";cropright "0.9937";cropbottom "0";filename
'Nblogo.wmf';file-properties "XNPEU";}}Reference Library}{}{}{%
../ReferenceIndex.tex}}
\end{tabular}
\end{center}

\noindent \hrulefill

\end{document}
