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Course Catalog 2012-2013
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 |
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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
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More precise information per implementation
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Contact teaching: 0 % Distance learning: 0 % Self-directed learning: 0 % |