Lectures related to General Linear Recurrence Relations

Linear Algebra Fundamentals

Explores linear algebra fundamentals, including key definitions, theorems, and practical applications in mathematics and technology.

Linear Algebra: Systems and Subspaces

Covers linear systems, vector subspaces, and the kernel and image of linear applications.

Linear Homogeneous Second Order Equations

Covers linear homogeneous second order differential equations and their solutions, including the concept of the Wronskian.

Distributions and Derivatives

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

Lines Spaces and Equivalent Matrices

Covers the concept of lines spaces and equivalent matrices in linear algebra.

Linear Applications: Bases and Dual Spaces

Explores bases, dual spaces, and linear applications in linear algebra.

Homogeneous Equations: Advanced Analysis II

Explores second-order linear scalar homogeneous equations in advanced analysis II.

Linear Mapping Basics

Covers the basics of linear mapping and coordinate systems.

Optimal Transport: Rockafellar Theorem

Explores the Rockafellar Theorem in optimal transport, focusing on c-cyclical monotonicity and convex functions.

Graph Sketching: Connected Components

Covers the concept of graph sketching with a focus on connected components.

Solutions of Homogeneous Linear Differential Equations

Covers the solutions of homogeneous linear differential equations and how to find linearly independent solutions.

Linear Independence and Bases

Covers linear independence, bases, and coordinate systems with examples and theorems.

Scalar Linear Higher Order ODEs: Properties and Solutions

Explores properties and solutions of scalar linear higher order ODEs with x-dependent coefficients and constant coefficients.

Functional Analysis I: Norms and Bounded Operators

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

Linear Independence and Basis

Explains linear independence, basis, and matrix rank with examples and exercises.

Homogeneous Linear Second-Order Differential Equations

Covers the solution of homogeneous linear second-order differential equations with constant coefficients and explores various cases of real and complex roots.

Theorems in Analysis

Covers the Meyers-Serrin theorem in analysis, discussing the conditions for functions in different spaces.

Linear Transformations: Matrices and Applications

Covers linear transformations using matrices, focusing on linearity, image, and kernel.

Linear Transformations: Polynomials and Bases

Covers linear transformations between polynomial spaces and explores examples of linear independence and bases.

Generalization Error

Explores generalization error in machine learning, focusing on data distribution and hypothesis impact.