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Legendre Transforms (Notes included)

The podcast explains Legendre transforms, a mathematical operation connecting functions of different variables. It details the transform's definition and geometrical interpretation, showing how it shifts between descriptions using conjugate variables, like position and momentum. The text covers one- and multivariable cases, providing examples and demonstrating its involutive property (applying it twice returns the original function). Finally, it highlights applications in thermodynamics (switching between potentials) and classical mechanics (Lagrangian to Hamiltonian formulation). Notes: https://github.com/PodcastLearn/Mathe...