Lectures related to Supporting Hyperplanes

Canonical Transformations: Hamilton-Jacobi Equation

Explores canonical transformations, the Hamilton-Jacobi equation, symplectic groups, and differential equations in physics.

Partial Derivatives and Functions

Covers partial derivatives for functions of one and two variables, emphasizing their importance and calculation.

Differentiability and Partial Derivatives

Explores differentiability in two variables and the chain rule for compositions.

Methods of Demonstrations: Recurrence and Differential Calculus

Covers methods of demonstrations and differential calculus of functions of several variables.

Functions of LR: Differentiability

Explains differentiability in LR functions and introduces the Jacobian matrix.

Differentiability and Hessians

Explores functions of class C^p, Hessian matrices, and methods to verify differentiability at a point.

Mathematical Complements: df or δf

Explores mathematical tools for differentials of functions of multiple variables and integrals, including conservative quantities and exact total differentials.

Taylor Polynomials and Function Properties

Covers Taylor polynomials, function properties, double integrals, partial derivatives, and function boundaries.