Core unitUnit 18 of 24
Functional Analysis
Explore infinite-dimensional vector spaces and operators that form the foundation of modern analysis and quantum mechanics.
Difficulty
Beginner
Estimated study
200 hours
Duration
Self-paced
Modules
0
Your progress
0%
Not started
Modules completed0 / 0
Estimated remaining≈ 200 hours
Modules coming soon
Sign in to save your progress.
About this unit
Unit overview
This unit extends linear algebra and analysis to infinite-dimensional spaces. You will study normed, Banach and Hilbert spaces together with linear operators, providing foundations for differential equations, optimisation and quantum theory.
Learning outcomes
What you’ll learn
- 01Work with normed, Banach and Hilbert spaces
- 02Analyse bounded linear operators and dual spaces
- 03Apply major results such as Hahn-Banach and Open Mapping
- 04Use orthogonality and spectral ideas in infinite-dimensional settings