Lecture

Advanced-analysis-ii

Related lectures (30)

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

Normed Spaces & Reflexivity

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

Properties of Weak Derivatives

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

The Banach Fixed Point Theorem

Explores the Banach Fixed Point Theorem, showing the uniqueness of fixed points in contraction mappings.

Approximation by Smooth Functions

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

Vector Spaces and Convergence

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

Functional Analysis and Distribution Theory

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

Interpolation Spaces

Explores interpolation spaces in Banach spaces, emphasizing real continuous interpolation spaces and the K-method.

Definition of Sobolew Spaces

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

Functional Analysis: Banach and Hilbert Spaces

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

Advanced Analysis II: Homogeneous ODEs and Banach Spaces

Explores the resolution of ODEs and the Banach fixed-point theorem.

Normed Spaces: Definitions and Examples

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

Interpolation Spaces

Explores interpolation spaces between Banach spaces and real interpolation spaces.

Nonlinear Equations: Fixed Point Method Convergence

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

Linear Operators: Boundedness and Convergence

Explores linear operators, boundedness, and convergence in Banach spaces, focusing on Cauchy sequences and operator identification.

Picard Method: Fixed Point Iterative Technique

Covers the Picard method for solving nonlinear equations using fixed point iteration.

Vector Spaces and Topology

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

Banach Spaces: Reflexivity and Convergence

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

Functional Analysis I: Foundations and Applications

Covers the foundations of modern analysis, introductory functional analysis, and applications in MAB111.

Analysis: Recap and Normed Space R^n

Covers a recap of Analysis 1 and 2, emphasizing normed space R^n, subsets, and continuous functions.