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# An Introduction to Functional Analysis

4 Reviews 342 students interested

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## Overview

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 for Coursera's An Introduction to Functional Analysis 4.3 Based on 4 reviews

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Did you take this course? Share your experience with other students.

• 1
Franck D
3.0 5 years ago
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.
2 people found
Martin N
4.0 3 years ago
completed this course.
Juliano I
5.0 3 years ago
by completed this course.
5.0 4 years ago
by is taking this course right now.