Lectures related to Fundamental Solutions of Laplace Equation

Fundamental Solutions of Laplace Equation

Covers the fundamental solutions of the Laplace equation and introduces distributions.

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Properties of Fundamental Solutions: Green's Representation Formula

Covers the properties of fundamental solutions and introduces Green's representation formula for solving partial differential equations.

Distributions and Laplace Transform: Key Concepts

Discusses distributions, the Laplace transform, and their applications in mathematical analysis.

Distributions & Interpolation Spaces

Covers distributions, interpolation spaces, convergence, and the concept of dual spaces.

Distribution & Interpolation Spaces

Covers the concept of distributions with compact support and their interpolation spaces.

Cut-off Phenomenon: Proof Ideas

Explores proof ideas related to the cut-off phenomenon and its implications in random walks on hypercubes.

Introduction to Distributions

Covers Green's representation formula, fundamental solutions, and distribution properties.

Signals & Systems I: Fourier Transformation and Distributions

Explores the Fourier transformation, Parseval relation, weak convergence, and generalized transformations in signals and systems.

Probability and Statistics

Covers probability distributions, moments, and continuous random variables.

Compression: Prediction

Covers the concepts of compression and prediction using prefix-free codes and distributions.

Fourier Transformation: Fundamentals

Covers the fundamentals of the Fourier transformation, including decreasing causal exponential signals and the Schwartz class.

Compression

Covers the concept of compression and constructing prefix-free codes based on given information.

Elements of Statistics: Probability and Random Variables

Introduces key concepts in probability and random variables, covering statistics, distributions, and covariance.

Elements of Statistics: Estimation & Distributions

Covers fundamental statistics concepts, including estimation theory, distributions, and the law of large numbers, with practical examples.

Basics of Risk Analysis and Management

Introduces the basics of risk analysis and management in civil engineering, covering distributions, statistical reminders, and mathematical interpretation techniques.

Probability Theory: Random Variables and Distributions

Introduces probability theory, random variables, and distributions, with a focus on their applications in atomic diffusion.

Signals & Systems I: Distributions and Linear Systems

Covers distributions, linear systems, impulse response, convolution, and examples of linear systems.

Common Distributions: Moment Generating Functions

Explores common probability distributions, special distributions, and entropy concepts.

Exponential Family: Distributions and Regularity

Covers the exponential family of distributions and the Ising model, explaining magnetism through dipoles and spins.