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Course Catalog 2014-2015
MAT-62256 Advanced Functional Analysis, 7 cr |
Additional information
Moodle is used during the course. The course is lectured every second year.
Suitable for postgraduate studies
Person responsible
Sirkka-Liisa Eriksson
Lessons
| Study type | P1 | P2 | P3 | P4 | Summer | Implementations | Lecture times and places |
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Requirements
Final exam or two partial exams
Completion parts must belong to the same implementation
Learning Outcomes
After completion of the course the student is mastering the foundations of the functional analysis the main results 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 theory Rieszin representation theorem | The proofs involving results connecting Lebesgue and the generalized measure theory | The proof of the Riesz represention theorem |
| 3. | Distribution theory and its applications to partial differential equations | The exact definition of tthe topology of the space of distributions | |
| 4. | Sobolev spaces |
Instructions for students on how to achieve the learning outcomes
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:
Study material
| Type | Name | Author | ISBN | URL | Edition, availability, ... | Examination material | Language |
| Book | Functional Analysis | G. Bachman, L. Narici | No | English | |||
| Book | Functional Analysis | Lax | No | English | |||
| Book | Functional Analysis | Rudin | No | English | |||
| Summary of lectures | MAT-53550 Advanced Functional Analysis | Eriksson | Yes | English |
Prerequisites
| Course | Mandatory/Advisable | Description |
| MAT-60206 Mathematical Analysis | Advisable | |
| MAT-61006 Introduction to Functional Analysis | Advisable | |
| MAT-61756 Measure and Integration | Advisable |
Prerequisite relations (Requires logging in to POP)
Correspondence of content
| Course | Corresponds course | Description |
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More precise information per implementation
| Implementation | Description | Methods of instruction | Implementation |