Functional Analysis Courses and Certifications

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Programming for the Planet - Functional Programming for Environmental Analysis

Explore functional programming's role in building resilient systems for climate analysis, addressing global crises through data-driven conservation and policy decisions.

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

Mathematical Algorithm in AI

Study ill-posed inverse problems through functional analysis, frequency-domain methods, forecasting, and energy-system applications.

• XuetangX
• Self-Paced
• Free Online Course

Measure Theory

Advanced study of abstract measures, Lebesgue integration, Borel and product measures, Lp spaces, and foundational measure-theoretic theorems.

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

IMSC;  NPTEL

Measure and Integration

Develops Lebesgue measure and integration from abstract measures through convergence, differentiation, product spaces, signed measures, and L^p spaces.

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

IMSC;  NPTEL

Sobolev Spaces and Partial Differential Equations

Develops Sobolev spaces and distribution theory for weak solutions of elliptic and evolution partial differential equations.

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

For the Love of Physics

Advanced Quantum Mechanics

Dive into advanced quantum mechanics concepts including Dirac notation, Hilbert spaces, operators, uncertainty principles, and the mathematical foundations of QM theory.

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

École Centrale Paris

An Introduction to Functional Analysis

4 ratings

Learn topology, metric and normed spaces, Banach and Hilbert spaces, the Riesz representation and Lax-Milgram theorems, Lp and Sobolev spaces, then simulate a membrane.

• Coursera
• 8 weeks, 6-8 hours a week
• No Longer Offered
• Paid Course

Steve Brunton

Infinite Dimensional Function Spaces and Fourier Series

Learn how functions form infinite-dimensional inner product spaces and provide orthogonal bases for Fourier series.

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

NPTEL-NOC IITM

Postulates of Quantum Mechanics - Part II: Quantum Observables and Time-evolution

Explore quantum observables and time-evolution in quantum mechanics, delving into advanced postulates and theoretical concepts.

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

NPTEL-NOC IITM

Orthogonality of Signals - Lecture 10

Explore orthogonality of signals, a fundamental concept in signal processing and communication systems. Gain insights into its applications and importance.

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

Physics Videos by Eugene Khutoryansky

Quantum Vector Projections and Complex Coefficients Visualization

Explore complex quantum vector projections through visual explanations, from basic coefficients to orthogonal functions and infinite-dimensional spaces.

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

Dr. Prinson P Samuel

Quantum Mechanics for MSc Chemistry - Semester 1

Master quantum mechanics fundamentals through postulates, operators, particle-in-box models, harmonic oscillators, and tunneling for MSc Chemistry students.

• YouTube
• 16 hours 10 minutes
• Self-Paced
• Free Video

Tobias Osborne

Mathematical Methods of Quantum Information Theory

Master the mathematical foundations essential for quantum information theory through comprehensive lectures covering key theoretical frameworks and computational techniques.

• YouTube
• 1 day 1 hour 20 minutes
• Self-Paced
• Free Video

IMSC;  NPTEL

Functional Analysis

A masters-level treatment of Banach and Hilbert spaces centered on weak and weak-* topologies, with applications to operator theory, Fourier series, and calculus of variations.

• Swayam
• 12 weeks
• No Longer Offered
• Free Online Course

Functional Analysis and its Applications

Explore normed, Banach, and Hilbert spaces, bounded operators, duality, and foundational theorems of functional analysis with applications.

• Swayam
• 12 weeks
• No Longer Offered
• Free Online Course