Course Catalog 2014-2015
Postgraduate

Basic Pori International Postgraduate Open University

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Course Catalog 2014-2015

MAT-61006 Introduction to Functional Analysis, 7 cr

Additional information

Suitable for postgraduate studies

Person responsible

Seppo Pohjolainen

Lessons

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


 


 
 3 h/week
 3 h/week
+3 h/week
+3 h/week


 
MAT-61006 2014-01 Tuesday 12 - 14 , TB215
Thursday 12 - 13 , SB204

Requirements

Two partial exams during the cource or final exam. Kaksi välikoetta tai tentti.

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 its properties. 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.     

Instructions for students on how to achieve the learning outcomes

Two partial exams during the course or final exam. Kaksi välikoetta tai tentti.

Assessment scale:

Numerical evaluation scale (1-5) will be used on the course

Study material

Type Name Author ISBN URL Edition, availability, ... Examination material Language
Book   Fuctional Analysis in Applied Mathematics and Engineering   Pedersen Michael       Chapman& Hall 2000   No    English  
Summary of lectures   Introduction to Functional Analysis   Pohjolainen Seppo         No    English  
Summary of lectures   Johdatus funktionaalianalyysiin   Pohjolainen Seppo         No    Suomi  

Additional information about prerequisites
Recommended prerequisite is BSc level mathematics major (or minor). Esitietoina suositellaan matematiikan pää tai sivuainetta kanditutkinnossa. Esitietoina suositellaan tekniikan kandidaatin matematiikan aineopintoja.

Prerequisite relations (Requires logging in to POP)



Correspondence of content

Course Corresponds course  Description 
MAT-61006 Introduction to Functional Analysis, 7 cr MAT-41146 Introduction to Functional Analysis, 7 cr  
MAT-61006 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-61006 2014-01       Contact teaching: 0 %
Distance learning: 0 %
Self-directed learning: 0 %  

Last modified13.01.2014