Course Catalog 2011-2012
International

Basic Pori International Postgraduate Open University

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Course Catalog 2011-2012

MAT-41146 Introduction to Functional Analysis, 7 cr

Additional information

Course home page is: http://matpc41.ee.tut.fi/JFA02
Suitable for postgraduate studies

Person responsible

Seppo Pohjolainen

Lessons

Study type P1 P2 P3 P4 Summer Implementations Lecture times and places
Excercises

 

 
 3 h/week
+3 h/week

 
MAT-41146 2011-01  

Requirements

Final examination or two partial examinations.

Learning outcomes

After passing the course the student - understands how mathematical analysis has developed recently. - knows the basic concepts of modern analysis and is able to operate with them. - is able to prove the most important theorems. - can apply the knowledge e.g. in solving integral equations

Content

Content Core content Complementary knowledge Specialist knowledge
1. Metric spaces and prperties. Continuous functions. Cauchy- sequences and completion of spaces. Fixed point theorem.     
2. General vector spaces and normed spaces. Basics of Banach spaces and operator theory in Banach spaces.     
3. Basics of Hilbert spaces. Operator theory in Hilbert spaces. Minimum norm theorem and Riesz reperesentation theorem.     
4. Spectral theory, especially for compact self-adjoint operators.     
5. Applications to integral equations.     

Study material

Type Name Author ISBN URL Edition, availability, ... Examination material Language
Book   Functional Analysis in Applied Mathematics and Engineering   Pedersen Michael       Chapman & Hall, 2000.      English  
Summary of lectures   Introduction to Functional Analysis   Seppo Pohjolainen       Lecture notes are available on the course home page.      English  

Additional information about prerequisites
Recommended prerequisite information consists of bachelor'studies in mathematics or in engineering mathematics. (matematiikan tai teknillisen matematiikan aineopinnot)

Prerequisite relations (Requires logging in to POP)



Correspondence of content

Course Corresponds course  Description 
MAT-41146 Introduction to Functional Analysis, 7 cr MAT-41140 Introduction to Functional Analysis, 7 cr  

More precise information per implementation

Implementation Description Methods of instruction Implementation
MAT-41146 2011-01       Contact teaching: 0 %
Distance learning: 0 %
Self-directed learning: 0 %  

Last modified14.02.2011