VARIATIONAL PRINCIPLES
Variational problems and variational principles. Convex functions. The Legendre transform. Constrained variation and Lagrange multipliers. Functionals and the Euler-Lagrange equation. First integrals and Fermat’s principle. Constrained variation of functionals . Hamilton’s principle. Symmetries and Noether’s theorem. PDEs from variational principles. The second variation. The Jacobi condition.
Variational Principles, by P. K. Townsend, 2018, University of Cambridge.
Variational Principles, written by D. Chua, based on lectures by P. K. Townsend, 2015, University of Cambridge.
Calculus of Variations, by J. Maynard, 2021, University of Oxford.
Brief Notes on the Calculus of Variations, by J. Figueroa-O’Farrill, University of Edinburgh.
- With Solutions
- Without Solutions
Variational Principles, M. Dunajski, 2021, University of Cambridge.Variational Principles, P. K. Townsend, 2015, University of Cambridge.
Calculus of Variations, by J. Maynard, 2021, University of Oxford.