Lectures related to Heat Kernel and Gaussian Analysis

Explores limits, convergence, and boundedness of functions and sequences.

Explores optimal transport in heat equations and metric spaces.

Covers continuous functions with compact support, density, and approximation, focusing on the heat equation.

Explores limits, divergence, and algebraic operations on sequences approaching infinity.

Explores the convergence and divergence of integrals, analyzing their behavior under specific limits.

Explains limits at right and left endpoints, convergence conditions, and function behavior near specific values.

Covers the convergence of fixed point methods for nonlinear equations, including global and local convergence theorems and the order of convergence.

Explores matrix operations, trends, and convergence conditions with a focus on clear definitions and examples.

Explores limits to infinity, including convergence, algebraic properties, and geometric progressions.

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

Explores probability convergence, discussing conditions for random variable sequences to converge and the uniqueness of convergence.

Covers implicit schemes in numerical analysis for solving partial differential equations.

Covers generalized integrals, convergence criteria, series convergence, and harmonic series in analysis.

Covers the basics of ordinary differential equations and their properties.

Explores implicit schemes in numerical analysis, emphasizing stability and convergence properties in solving differential equations.

Covers the limited development of integration and methods for calculating the limit development of functions and antiderivatives.

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

Covers Markov chains, focusing on reversibility, convergence, ergodicity, and applications.

Covers properties of logarithmic functions, series convergence, and the Riemann integral.

Covers iterative methods for solving linear equations and analyzing convergence, including error control and positive definite matrices.