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Course Catalog 2013-2014
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 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 % |