Functional Analysis Courses and Certifications

Introduction to Functional Analysis

Work through normed and Hilbert spaces: prove the Hahn-Banach, open mapping and spectral theorems, build Lebesgue measure and integration, and analyze compact self-adjoint operators.

• MIT OpenCourseWare
• Self-Paced
• Free Online Course

The Bright Side of Mathematics

Functional Analysis

Study metric, normed, and inner-product spaces through Banach and Hilbert spaces, bounded operators, duality, and spectral theory.

• YouTube
• 4 hours 30 minutes
• Self-Paced
• Free Video

Real and Functional Analysis

Nella prima parte del corso introdurremo gli spazi metrici, normati e di Banach. In particolare, definiremo gli spazi di Hilbert e ne descriveremo le principali proprietà. In particolare, vedremo che

• Federica
• Self-Paced
• Free Online Course

IISc Bangalore;  NPTEL

C* Algebras and Spectral Theorem

Proves the spectral theorem for bounded normal operators through C*-algebras and projection-valued measures.

• Swayam
• 8 weeks
• Available until Oct 9, 2026
• Free Online Course

NPTEL-NOC IITM

The Banach Fixed Point Theorem

Explore the Banach fixed point theorem, a fundamental concept in functional analysis with applications in various mathematical fields.

• YouTube
• 14 minutes
• Self-Paced
• Free Video

For the Love of Physics

Introduction to Hilbert Spaces in Quantum Mechanics

Explore the mathematical foundations of quantum mechanics through Hilbert spaces, covering vector operations, inner products, norms, and completeness principles essential for understanding quantum states.

• YouTube
• 35 minutes
• Self-Paced
• Free Video

NPTEL-NOC IITM

Spectral Mapping Theorem for Normal Operators - Continuous Functions

Explore the spectral mapping theorem for normal operators and its applications to continuous functions in operator theory.

• YouTube
• 19 minutes
• Self-Paced
• Free Video

The Bright Side of Mathematics

Distribution Theory

An introduction to distributions as generalized functions, from test functions and convergence to delta distributions, vector-space structure, smooth multiplication, and coordinate transformations.

• YouTube
• 1 hour 30 minutes
• Self-Paced
• Free Video

Business Analysis: Functional & Non-Functional Requirements

9479 ratings at Udemy

Learn Requirements Decomposition / Drill-Down Techniques, Then Judge If AI Output is Right, Wrong, or Just Sounds Good

• Udemy
• 1 hour 36 minutes
• Self-Paced
• Paid Course

应用泛函分析

从Lebesgue测度与积分出发，系统学习Banach、Hilbert空间及有界算子的谱、紧性和自伴性。

• XuetangX
• Self-Paced
• Free Online Course

泛函分析

以具体空间和线性算子为例，系统学习距离空间、巴拿赫空间、希尔伯特空间及有界线性算子的基本理论。

• XuetangX
• Self-Paced
• Free Online Course

泛函分析

通过板书详解定理证明，系统学习无穷维空间中的算子理论、Banach空间与Hilbert空间。

• XuetangX
• Self-Paced
• Free Online Course

泛函分析

你是否想达到能用分析的、代数的和拓扑相结合的数学思维方法综合处理问题？本门课程的目的就是帮助更多人学会高维空间中处理线性问题的分析方法，从而进一步提高自已的数学思维水平。

• XuetangX
• Self-Paced
• Free Online Course

USENIX

Functional Resonance Analysis - Diagramming Your System

Explore the Functional Resonance Analysis Method to model complex systems, understand their interactions, and identify sources of success and risks in constantly changing environments.

• YouTube
• 20 minutes
• Self-Paced
• Conference Talk

GOTO Conferences

Data Analysis with Vector Functional Programming - A Tour of the Q Programming Language

Explore vector functional programming for data analysis using Q language. Learn key concepts, syntax, and practical applications for efficient data manipulation and analysis.

• YouTube
• 26 minutes
• Self-Paced
• Free Video