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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. |

*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 |

课程主页: https://www.coursera.org/course/functionalanalysis

Explore 1600+ online courses from top universities. Join Coursera today to learn data science, programming, business strategy, and more.课程评论: 1 个评论

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

0 |
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. |