MAT-61006 Introduction to Functional Analysis, 7 cr

Additional information

Kurssin kotisivu on Moodlessa: https://moodle2.tut.fi
Suitable for postgraduate studies

Person responsible

Sirkka-Liisa Eriksson

Lessons

Implementation 1: MAT-61006 2015-01

Study type P1 P2 P3 P4 Summer

Lectures
Excercises

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

Lecture times and places: Thursday 12 - 14 TB215 , Tuesday 12 - 15 TB215 , Wednesday 13 - 16 TD308

Requirements

Twomidterml exams during the course 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 midterm 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 Additional information Examination material

Book Fuctional Analysis in Applied Mathematics and Engineering Pedersen Michael Chapman& Hall 2000 No

Summary of lectures Introduction to Functional Analysis Pohjolainen Seppo No

Summary of lectures Johdatus funktionaalianalyysiin Pohjolainen Seppo No

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.

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

Last modified 28.12.2015

Study type	P1	P2	P3	P4	Summer
Lectures Excercises			4 h/week 3 h/week	+3 h/week +3 h/week

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.

Type	Name	Author	ISBN	URL	Additional information	Examination material
Book	Fuctional Analysis in Applied Mathematics and Engineering	Pedersen Michael			Chapman& Hall 2000	No
Summary of lectures	Introduction to Functional Analysis	Pohjolainen Seppo				No
Summary of lectures	Johdatus funktionaalianalyysiin	Pohjolainen Seppo				No

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