index of differential equationsIndexOfDifferentialEquations2005-05-07 15:38:402009-08-06 15:12:09Topicdifferential equation% this is the default PlanetMath preamble. as your knowledge
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\newtheorem{thm}{Theorem}
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\newtheorem{cor}{Corollary}\subsubsection*{Differential equations for functions on $\R$ }
\begin{enumerate}
\item General solution, particular solutions, singular solution
\item \PMlinkname{Equation\, y'' = f(x)}{EquationYFx}
\item Separation of variables
\item ODE types reductible to the variables separable case
\item Exact differential equation
\item Linear differential equation of first order
\item Second order linear differential equation with constant coefficients
\item General solution of linear differential equation
\item Frobenius method
\item Bessel's equation
\item Chebyshev equation
\item Hermite equation
\item van der Pol equation
\item Hypergeometric equation
\item \PMlinkname{Laguerre's differential equation}{LaguerrePolynomial}
\item Second order ordinary differential equation
\item Bernoulli equation
\item \PMlinkname{d'Alembert's equation}{DAlembertsEquation}
\item Clairaut's equation
\item Riccati equation
\end{enumerate}
\subsubsection*{Ordinary differential equations}
\begin{enumerate}
\item Linear ordinary differential equations
\item Differential equation of the isogonal trajectories, the tilt curves
\item Frenet equations
\item \PMlinkname{Hamilton equations}{HamiltonianEquations}
\item Geodesic equation
\item Gradient system
\item Lorenz equation
\end{enumerate}
\subsubsection*{Partial differential equations}
\begin{enumerate}
\item Gradient system
\item \PMlinkname{Euler-Lagrange equations}{EulerLagrangeDifferentialEquation}
\item Hamilton equations
\item Heat equation
\item Laplace equation
\item Poisson's equation
\item Wave equation
\item \PMlinkname{d'Alembert and D. Bernoulli solutions of wave equation}{DAlembertAndDBernoulliSolutionsOfWaveEquation}
\item Helmholtz equation
\item Maxwell's equations
\item Korteweg - de Vries equation
\item Schr\"odinger's wave equation
\item Dirac equation
\item Klein-Gordon equation
\item Hamilton-Jacobi equation
\item Telegraph equation
\item Black-Scholes equation
\item Solved examples:\\
a) example of solving the heat equation\\
b) time-dependent example of heat equation\\
c) using Laplace transform to solve heat equation\\
d) \PMlinkname{solving the wave equation due to D. Bernoulli}{SolvingTheWaveEquationByDBernoulli}
\end{enumerate}
\subsubsection*{Complex}
\begin{enumerate}
\item Beltrami differential equation
\item Cauchy-Riemann equations
\end{enumerate}