Course Catalog 2011-2012
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Basic Pori International Postgraduate Open University

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Course Catalog 2011-2012

MAT-53557 Advanced Functional Analysis, 8 cr

Additional information

The course is the English version of the Finnish course MAT-53551. The language of the lectures depends on how many English speaking students are attending. Homework and instructed exercises are in English
Suitable for postgraduate studies
Will not be lectured year 2011-2012

Person responsible

Sirkka-Liisa Eriksson

Requirements

Final exam or two partial exams
Completion parts must belong to the same implementation

Principles and baselines related to teaching and learning

During the course there are instructed exercises that helps learning. Moodle study platform is used during the course and extra material may be handed out through that there and students may discuss about there problem.

Learning outcomes

After completion of the course the student is mastering the topological foundations of the functional analysis and is capable of deducing them from the definitions. The student can compute the generalized derivatives and apply them for solving partial differential equations. The student can explain different type of Sobolev spaces and knows their importance.

Content

Content Core content Complementary knowledge Specialist knowledge
1. Topological foundations Banach- ja Hilbert spaces Hahn-Banach theorem The open mapping theorem Baire category theorems Closed operator theorems   Weak topology.   
2. Generalized measure theoryY Rieszin representaion theorem  The proofs involving results connecting Lebesgue and the generalized measure theory  The proof of the Riesz represention theorem 
3. Distirbution theory and its applications to partial differential equations    The exact definition of the distribution space topology 
4. Sobolev spaces     

Evaluation criteria for the course

The grade of the course is based on the final exam or two partial exams. When the points for the final exam or the partial exams are 30% of the maximum, the grade of the course may be improved by bonus points collected from the instructed exercises and homework. The passing limit is 50% of the maximum. If the student is mastering the concepts, results, short proofs and examples type of problems the evaluation is 3. For the grade 4 the student should in addition to the previous level be able to independently apply theory more. For the grade 5 the student should independently deduce results, invent solutions and compare results more than in the previous levels.

Assessment scale:

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

Partial passing:

Completion parts must belong to the same implementation

Study material

Type Name Author ISBN URL Edition, availability, ... Examination material Language
Book   Functional Analysis   G. Bachman, L. Narici            English  
Book   Functional Analysis   Lax            English  
Book   Functional Analysis   Rudin            English  
Summary of lectures   MAT-53550 Advanced Functional Analysis   Eriksson            English  

Prerequisites

Course Mandatory/Advisable Description
MAT-41140 Johdatus funktionaalianalyysiin Advisable    
MAT-41146 Introduction to Functional Analysis Advisable    
MAT-41291 Mitta- ja integraaliteoria Advisable    
MAT-41297 Measure and Integral Theory Advisable    
MAT-43850 Matemaattinen analyysi 2 Advisable    

Prerequisite relations (Requires logging in to POP)



Correspondence of content

Course Corresponds course  Description 
MAT-53557 Advanced Functional Analysis, 8 cr MAT-53556 Advanced Functional Analysis, 7 cr  

Last modified28.02.2011