Lectures related to Integrable system

Explores canonical equations, integrable systems, trajectories, and the symplectic matrix in understanding system dynamics.

Explores negligible sets, integrable sets, and almost everywhere concept in mathematical analysis.

Explores exact linearization, determining conditions and transformations using Lie bracket and hook of Lie.

Explores canonical transformations in Hamiltonian mechanics, emphasizing variable separation in the Hamilton-Jacobi equation.

Covers a recap of improper integrals and bounded functions.

Explains the Fubini theorem for closed sets and volume calculations.

Covers generalized integrals, focusing on convergence conditions and examples.

Explores changing variables in double integrals and applying Fubini's theorem in R² for simplifying calculations.

Explores characterizations and generalizations of the Riemann integral, showcasing its properties and applications.

Discusses integrability, square-integrability, boundedness, centering, and linearity of random variables.

Explores the Fubini theorem for integrability in two variables and emphasizes the significance of the order of integration.

Explores the properties of conditional expectation and its extension to positive variables.

Explores uniform integrability, convergence theorems, and the importance of bounded sequences in understanding the convergence of random variables.

Covers the properties of Riemann integrals and comparisons between integrals.

Covers the properties of Riemann integrals and introduces the concept of average value of a function.

Explores continuous functions and integrability through practical examples.

Introduces Lp spaces, covering norms, inequalities, and integrability of functions.

Explores cylindrical coordinates, integrability, and volume calculations using examples.

Covers the integration of functions in several variables, Darboux sums, and Fubini's theorem on a closed box.

Covers integrability, anti-derivatives, and integration by parts in calculus.