An Introduction to Functional Analysis

开始时间: 09/12/2014 持续时间: 8 weeks

所在平台: Coursera

课程类别: 数学

大学或机构: École Centrale Paris(巴黎中央理工学院)

授课老师: John Cagnol



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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.


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: Lp spaces; Fischer-Riesz
Week 7: Sobolev spaces
Week 8: Use of functional analysis for Partial Differential Equations



Tensorspace 2014-09-13 17:58 0 票支持; 0 票反对

One of my professor told me: you'd better learn some functional analysis or real analysis despite of all math courses you've taken in undergraduate years.

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巴黎中央理工学院 泛函 泛函分析 泛函分析介绍 泛函分析导论 数学