Legendre Transform as Duality Between Points and Tangent Lines
LegendreTransform Duality TangentLines
02:00 Abide by Reason introduces the Legendre transform for learners who know derivatives and tangent lines but have not seen how they can encode a whole function.
Convexity, Monotonicity, and When Legendre Transforms Exist
ConvexFunctions MonotoneDerivatives TransformConditions
08:30 This note is for learners who want to know for which functions the Legendre transform is well-defined and invertible.
Multivariable Legendre Transform and Variable Swaps
MultivariableLegendre VariableSwaps DifferentialForms
12:30 Abide by Reason extends the Legendre transform to multivariable functions for learners ready to see how whole sets of variables can be swapped.
Thermodynamic Potentials as Legendre Transforms of Internal Energy
ThermodynamicPotentials InternalEnergy HelmholtzFreeEnergy
18:30 This note is for learners connecting the abstract Legendre transform to the zoo of thermodynamic potentials and their natural variables.
Legendre Transform in Classical Mechanics: From Lagrangian to Hamiltonian
LagrangianToHamiltonian CanonicalVariables HamiltonsEquations
23:30 Abide by Reason ties the Legendre transform back to classical mechanics for viewers already familiar with Lagrangian dynamics.