An Introduction to Functional Analysis
École Centrale Paris via Coursera
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Overview
Class Central Tips
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 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
Taught by
John Cagnol
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Reviews
4.3 rating, based on 4 reviews
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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.
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Juliano Ignacio completed this course.
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Martin Nilsson completed this course.