Temple University 3 credits MATH
The course covers the first variation and Euler-Lagrange equations, including null Lagrangians and Caratheodory's "Royal Road". It introduces geodesic coverings, the eikonal equation, and the Hamilton-Jacobi equation. The second variation is explored through Jacobi's theory of conjugate points and Weierstrass's E-function. The Hamiltonian formalism, convex duality, and Hilbert's invariant integral are also discussed, highlighting connections between variational principles, geometry, and physics.
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