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\title{m 5500 Calculus of Variations: 
Syllabus. }
\author{Andrej Cherkaev. Spring 2013 MWF, JWW 308, 3:05-3:55}
\date{}
\maketitle
\begin{enumerate}
\item Introduction: History. Minimization Problems. Methods. 
\item First variation. Applications to physics, geometry, and approximations.
\begin{enumerate}
\item Euler equation. Smooth approximatic, geometric optics.
\item Euler-Lagrange equation (multiple integrals). Variational principles: Conductivity, elasticity.
\item Variation of boundary terms. Examples (distance to a surface, cooling boundary conditions, extreme loading)
\item Constrained minimum. Lagrange mutlipliers (isoperimetric and pointwise constraints). Introduction to Lagrangian mechanics. 
\item Variation of the domains. Examples from geometry and physics. 
\end{enumerate}
\item Legendre, Jacobi, Weierstrass conditions for one- and multivariable integrals. Ill-posed problems, regularization and relaxation. Examples. 

%\item Legandre, Jacobi, Weierstrass conditions for multiple integrals
\item Convexity. Duality. Legendre transform. Dual variational princtiples. Hamiltonian.

 \item Minimizing sequences and numerical methods. Numerical example. 
\item Isoperimetric problem. History, geometric methods. 
\item Existence and uniqueness theorems. Overview. 
\item Nonconvex problems. Oscillationg minimizers. Quasiconvexity
\item Two examples of relaxation.
\end{enumerate} 


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