Lectures related to Bounded variation

Semimartingale: Joint Variation Process

Covers semimartingales, Ito's lemma, and polynomial demonstrations, emphasizing the management of second-order terms and induction reasoning.

Multivariable Integral Calculus

Covers multivariable integral calculus, including rectangular cuboids, subdivisions, Douboux sums, Fubini's Theorem, and integration over bounded sets.

Banach Spaces: Reflexivity and Convergence

Explores Banach spaces, emphasizing reflexivity and sequence convergence in a rigorous mathematical framework.

Compact Embedding: Theorem and Sobolev Inequalities

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

Functional Calculus: Simple Functions

Covers the extension of functional calculus to simple functions and the concept of *-homomorphism.

Doob's Decomposition Theorem

Covers Doob's decomposition theorem for submartingales and explores Brownian motion properties, quadratic variation, and continuous martingales.

Stochastic Integration: First Steps

Covers stochastic integration, process bracket, martingales, and variations in submartingales.

Functional Analysis I: Norms and Bounded Operators

Explores norms and bounded operators in functional analysis, demonstrating their properties and applications.

Dynamical System Theory for Engineers: Large Scale Stability

Explores large scale stability in dynamical systems, emphasizing non-increasing trajectories and strict decrease of a specific function.

Dynamical System Theory for Engineers: Large Scale Stability

Covers the concept of large scale stability in dynamical systems.

Gaussian Curvature in Plates

Explores Gaussian curvature, principal curvatures, and nonlinear strain in thin elastic plates.

Advanced analysis II: riemann integral properties

Explores advanced Riemann integral properties, including integrability, sums, and partitions.

Derivatives and Local Extrema

Explores derivatives, local extrema, and function variation in mathematical analysis.

Weak Derivatives: Definition and Properties

Covers weak derivatives, their properties, and applications in functional analysis.

Advanced Analysis II: Riemann Integrability and Jordan Measure

Explores Riemann integrability and Jordan measure, discussing the conditions for a set to be negligible.

Advanced Analysis II: Integrals and Functions

Covers advanced topics in analysis, focusing on integrals, functions, and their properties.

Theorem of the Average

Explores the Theorem of the Average, integrability criteria, properties of the integral, and volume concepts.

Fubini's Theorem: Multiple Integrals

Explores Fubini's Theorem for multiple integrals, emphasizing the n=2 case.

Improper Integrals: Recap and Bounded Functions

Covers a recap of improper integrals and bounded functions.

Dynamical Approaches to Spectral Theory of Operators

Explores dynamical approaches to the spectral theory of operators, focusing on self-adjoint operators and Schrödinger operators with dynamically defined potentials.