An Introduction to Functional Analysis is an online course conducted by the École Centrale Paris.
About the course
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.
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
The course is mostly self-contained; however, students need to be familiar with functions, derivatives and integrals.
September 12, 2014 - November 28, 2014
For further information, click here.