Func. Analysis·Course
Functional Analysis
Functional analysis: normed spaces, Banach and Hilbert spaces, operators, and spectral theory
5
Modules
15
Articles
~2 h
Reading
IV
CLOs
§ 01 — Curriculum
5 modules.
Each module is a small unit. Most read in sequence — but a determined reader can begin anywhere.
- M IMetric and Normed SpacesMetrics, norms, completeness, and convergence in function spaces3 articles
18 minBegin → - M IIHilbert SpacesInner product, orthogonality, and Fourier series3 articles
18 minBegin → - M IIIOperator TheorySpectral theory, compact operators, and Fredholm equations3 articles
18 minBegin → - M IVVariational MethodsWeak solutions, the Lax–Milgram theorem, and Sobolev spaces3 articles
18 minBegin → - M VFourier Transforms and DistributionsFourier transform, Plancherel’s theorem, and generalized functions3 articles
18 minBegin →
§ 02 — Learning outcomes
4 outcomes.
CLO I
Metric Spaces
Work with metric, normed, and Banach spaces
CLO II
Hilbert Spaces
Understand orthogonality, bases, and projections in Hilbert spaces
CLO III
Linear Operators
Analyze bounded and closed operators and apply the Hahn–Banach theorem
CLO IV
Spectral Theory
Study operator spectra and compact and self-adjoint operators
§ 03 — Practices