Class Central is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

# An Introduction to Functional Analysis

Social Learning for Open Courses

Join one of our cohorts to learn from instructors, experts, or each other with weekly live streams.

## Overview

##### Class Central Tips
Functional analysis is the branch of mathematics dealing with spaces of functions. It is a valuable tool in theoretical mathematics as well as engineering. It is at the very core of numerical simulation.

In this class, I will explain the concepts of convergence and talk about topology. You will understand the difference between strong convergence and weak convergence. You will also see how these two concepts can be used.

You will learn about different types of spaces including metric spaces, Banach Spaces, Hilbert Spaces and what property can be expected. You will see beautiful lemmas and theorems such as Riesz and Lax-Milgram and I will also describe Lp spaces, Sobolev spaces and provide a few details about PDEs, or Partial Differential Equations.

## Syllabus

Week 1: Topology; continuity and convergence of a sequence in a topological space.
Week 2: Metric and normed spaces; completeness
Week 3: Banach spaces; linear continuous functions; weak topology
Week 4: Hilbert spaces; The Riesz representation theorem
Week 5: The Lax-Milgram Lemma
Week 6: Properties of the Lp spaces
Week 7: Distributions and Sobolev Spaces
Week 8: Application: simulating a membrane

John Cagnol

## Reviews

4.2 rating, based on 4 reviews

Start your review of An Introduction to Functional Analysis

• Franck Dernoncourt
3

Franck Dernoncourt is taking this course right now, spending 4 hours a week on it and found the course difficulty to be medium.

This is a pretty good course (French teachers are often good at maths) but I'm not enjoying the peer assessment there.
• Soumyadipta Das is taking this course right now.

• Juliano Ignacio completed this course.

• Martin Nilsson
3

Martin Nilsson completed this course.

### Never Stop Learning!

Get personalized course recommendations, track subjects and courses with reminders, and more.