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Concept

Distribution (mathematics)

Related lectures (30)

Functional Analysis and Distribution Theory

Explores different notions of function equality, linear functionals, operations on distributions, and the advantages of working with Schwartz' space.

Quadratic Forms and Hecke Operators

Explores quadratic forms, Hecke operators, eigenvalues, and compactly supported functions in matrix theory.

Functional Analysis and Distribution Theory

Introduces functional analysis, distribution theory, topological vector spaces, and linear operators, emphasizing their importance in engineering applications.

Continuous Random Variables

Explores continuous random variables, density functions, joint variables, independence, and conditional densities.

Spatial Topological Queries MOOC: Geographical Information Systems 1

Explores topology, test functions, and space operators for spatial queries.

Brownian Motion: Fundamentals and Applications

Explores the fundamentals of Brownian motion, including particle positions and distribution functions.

Cut-off Phenomenon: Proof Ideas

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

Collisionless Systems Equilibrium

Explores collisionless systems equilibrium, anisotropic distribution functions, Jeans Equations, and models with finite potential.

Exponential Family: Distributions and Regularity

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

Conditional Density and Expectation

Covers conditional density, independence of random variables, expectation, and variance calculation.

Quantum Transport: Scattering Matrix Approach

Explores quantum transport using the scattering matrix approach to analyze conductance and resistance in electron movement.

Collisionless Boltzmann Equation

Explores the Collisionless Boltzmann Equation, Jeans theorems, and equilibria of collisionless systems, focusing on connections between barotropic fluids and ergodic stellar systems.

Distributions and Derivatives Log in to Mediaspace to watch this video

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

Convolution and Fourier Transform Log in to Mediaspace to watch this video

Explores convolution properties, heat equation application, and Fourier transform on tempered distributions.

Fundamental Solutions of Laplace Equation Log in to Mediaspace to watch this video

Explores fundamental solutions, Green's formula, distributions, and convergence in Laplace equation.

Probability Theory: Random Variables and Distributions Log in to Mediaspace to watch this video

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

Distribution & Interpolation Spaces Log in to Mediaspace to watch this video

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

Properties of Fundamental Solutions: Green's Representation Formula Log in to Mediaspace to watch this video

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

Martingales and Brownian Motion: Reflection Principle Log in to Mediaspace to watch this video

Explores the reflection principle in martingales and Brownian motion, simplifying probability calculations.

Distributional Derivatives Log in to Mediaspace to watch this video

Explores distributional derivatives, continuity, boundedness of linear operators, and weak-* continuity.