Home » Course Layouts » Free Course Layout Udemy
G14FUN - Functional Analysis (University of Nottingham). This is a collection of video lectures taught by Dr. Joel Feinstein. Functional analysis begins with a marriage of linear algebra and metric topology. These work together in a highly effective way to elucidate problems arising from differential equations.
0
2
English
English [CC]
- Learn basic syntax that can apply to any language.
- Learn what is a programming language and the basic concepts for beginners.
- Understand what is Javascript in it's truest form.
- Know the basic syntax of Javascript.
- Know some hidden quirks in Javascript.
Description
Solutions are sought in an infinite dimensional space of functions. This module paves the way by establishing the principal theorems (all due in part to the great Polish mathematician Stefan Banach) and exploring their diverse consequences. Topics to be covered will include: norm topology and topological isomorphism; boundedness of operators; compactness and finite dimensionality; extension of functionals; weak*-compactness; sequence spaces and duality; and basic properties of Banach algebras. (from unow.nottingham.ac.uk)
Course content
- Lecture 01 – Functional Analysis – Totally Ordered Sets and Partially Ordered Sets Unlimited
- Lecture 02 – Complete Metric Spaces Unlimited
- Lecture 03 – Revision of Metric and Topological Spaces Unlimited
- Lecture 04 – Complete Metric Spaces II – Proof of the Baire Category Theorem Unlimited
- Lecture 5a – Nowhere Dense Sets Unlimited
- Lecture 5b – Infinite Products and Tychonoff’s Theorem Unlimited
- Lecture 6a – Discussion Session on Partially Ordered Sets and Vector Spaces Unlimited
- Lecture 6b – Discussion Session on Partially Ordered Sets and Vector Spaces (cont.) Unlimited
- Lecture 07 – Infinite Products and Tychonoff’s Theorem Unlimited
- Lecture 08 – The Proof of Tychonoff’s Theorem Unlimited
- Lecture 9a – Infinite Products and Tychonoff’s Theorem Unlimited
- Lecture 9b – Normed Spaces and Banach Spaces Unlimited
- Lecture 10 – Normed Spaces and Banach Spaces Unlimited
- Lecture 11a – Completeness of the Uniform Norm Unlimited
- Lecture 11b – A Revision Interlude on Pointwise and Uniform Convergence Unlimited
- Lecture 12 – Normed Spaces and Banach Spaces Unlimited
- Lecture 13a – Normed Spaces and Banach Spaces Unlimited
- Lecture 13b – Equivalence of Norms Unlimited
- Lecture 14a – A Recap of Equivalence of Norms Unlimited
- Lecture 14b – A Recap of Equivalence of Norms Unlimited
- Lecture 15a – Final Discussion of Equivalence of Norms Unlimited
- Lecture 15b – Linear Maps Unlimited
- Lecture 16a – Linear Maps and Connections with Lipschitz Continuity Unlimited
- Lecture 16b – Sequence Spaces Unlimited
- Lecture 17 – Sequence Spaces (cont.) Unlimited
- Lecture 18a – More about Sequence Spaces Unlimited
- Lecture 18b – Isomorphisms Unlimited
- Lecture 19a – Isomorphisms of Normed Spaces Unlimited
- Lecture 19b – Sums and Quotients of Vector Spaces Unlimited
- Lecture 20a – Sums and Quotients of Vector Spaces (cont.) Unlimited
- Lecture 20b – Dual Spaces Unlimited
- Lecture 21 – Duals and Double Duals Unlimited
- Lecture 22 – Conclusion of Dual Spaces Unlimited
- Lecture 23 – Extensions of Linear Maps Unlimited
- Lecture 24 – Completions, Quotients, and Riesz’s Lemma Unlimited
- Lecture 25 – The Weak-* Topology and the Banach-Alaoglu Theorem Unlimited
- Lecture 26 – Open Mappings and Their Applications Unlimited
- Lecture 27 – Applications of the Open Mappings Lemma Unlimited
- Lecture 28a – Recap Concerning Convex Sets which are Symmetric about 0 Unlimited
- Lecture 28b – Recap, Proof of the Opening Mapping Theorem Unlimited
- Lecture 29a – Recap, and Proof of the Closed Graph Theorem Unlimited
- Lecture 29b – The Uniform Boundedness Principle/Banach-Steinhaus Unlimited
- Lecture 30 – Commutative Banach Algebras Unlimited
- Lecture 31 – Commutative Banach Algebras Unlimited
- Lecture 32 – Discussion Session on the Measure Theory Unlimited
Instructor
