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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 |
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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
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More precise information per implementation
| Implementation | Description | Methods of instruction | Implementation |
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Contact teaching: 0 % Distance learning: 0 % Self-directed learning: 0 % |