Lectures related to Recurrence on Two Variables

Covers methods of demonstrations and the Taylor formula for functions of several variables.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Introduces gradient, Laplacian, Taylor formula, polynomial approximations, extrema, and Taylor series expansions in multiple variables.

Covers mechanics concepts in different coordinate systems, explaining position, velocity, and acceleration vectors.

Covers position, velocity, and acceleration in polar, cylindrical, and spherical coordinate systems.

Introduces Cartesian product and induction for proofs using integers and sets.

Explores position, velocity, and acceleration in polar and cylindrical coordinate systems, simplifying complex formulas for motion analysis.

Covers proof techniques including direct proof, contraposition, contradiction, cases, and counterexample.

Explores differentiability, coordinate changes, Jacobian determinant, gradient transformation, and chain rule.

Explores circular motion, friction, and Newton's laws in various coordinate systems.

Covers polar coordinates, the Jacobian matrix, and examples of calculating areas in polar coordinates.

Covers the fundamental concepts of kinematics, including position, velocity, and acceleration in different coordinate systems.

Explores rotating vectors in physics, emphasizing the norm-angular speed relationship and various coordinate systems.

Explores the Laplacian, Riemannian metric, and invariant operators in hyperbolic surfaces.

Explores the Laplacian operator in Cartesian and polar coordinates, showcasing its application through examples.

Explores Bourgain's theorem on sparsest cut in graphs, emphasizing semimetrics and cut optimization.

Explores local diffeomorphisms and their properties, including local inverses and neighborhood mappings.

Covers cylindrical and spherical coordinates, transformations between coordinate systems, and rotations in physics.

Explores optimal transport in heat equations and metric spaces.