Lecture

Analysis: Recap and Normed Space R^n

Related lectures (30)

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Approximation by Smooth Functions

Discusses approximation by smooth functions and the convergence of function sequences in normed vector spaces.

Normed Spaces & Reflexivity

Covers normed spaces, Banach spaces, and Hilbert spaces, as well as dual spaces and weak convergence.

Normed Spaces: Definitions and Examples

Covers normed vector spaces, including definitions, properties, examples, and sets in normed spaces.

Vector Spaces and Convergence

Covers vector spaces, compact sets, convergence, continuity, and uniqueness theorems.

Definition of Sobolew Spaces

Explains the definition of Sobolew spaces and their main properties, focusing on weak denivelre.

Preliminaries in Measure Theory

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Function Approximations

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

Vector Spaces and Topology

Covers normed vector spaces, topology in R^n, and the principle of drawers as a demonstration method.

Properties of Complete Spaces

Covers the properties of complete spaces, including completeness, expectations, embeddings, subsets, norms, Holder's inequality, and uniform integrability.

Distributions and Derivatives

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

Properties of Weak Derivatives

Explores weak derivatives in Sobolev spaces, discussing their properties and uniqueness.

Generalized Integrals: Type 2

Covers the integration of limit expansions and continuous functions by pieces.

Analysis IV: Convergence and Approximation in L² Space

Explores convergence and approximation in L² space, emphasizing the limitations of continuous functions and the importance of closed sets.

Banach Spaces: Reflexivity and Convergence

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

Functional Analysis: Banach and Hilbert Spaces

Covers Banach and Hilbert spaces, separability, norm, continuity, and functional analysis.

Advanced Analysis II: March 23

Covers variable bounds, convergence of integrals, and homomorphisms in advanced analysis.

Norms and Convergence

Covers norms, convergence, sequences, and topology in Rn with examples and illustrations.

Vector Spaces and Topology

Covers vector spaces, topology, and proof methods like the pigeonhole principle in R^n.

Lp Spaces: Introduction

Introduces Lp spaces, covering norms, inequalities, and integrability of functions.