MATH 542 Calculus of Variations
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The above-stated course is all about the introduction to calculus of variations. The course is quite wide and embraces topics, such as, variation of a functional, the Euler-Lagrange equations, canonical transformations, parametric forms, end points, the Hamilton-Jacobi equation, the second variation and the principle of least action and conservation laws.
Topic outline:
1. Minimizing in exceedingly linear space; directional derivatives; biconvex functions.
2. Convex useful and calculus of variations; variations; spare conditions for a minimum of biconvex functional -- the Leonhard Euler Lagrange equation; applications in mechanics and minimum space issues.
3. The lemmas of DuBois-Raymond.
4. Minimizing while not previous assumptions of smoothness, the Euler-Lagrange equations once more.
5. Optimizing with relevance piecewise swish functions; general linear area background, norms; the Weierstrass corner conditions.
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