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Course Catalog 2012-2013
MAT-53557 Advanced Functional Analysis, 8 cr |
Additional information
The course is the English version of the Finnish course MAT-53551. The language of the lectures depends on how many English speaking students are attending. Homework and instructed exercises are in English
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
Principles and baselines related to teaching and learning
During the course there are instructed exercises that helps learning. Moodle study platform is used during the course and extra material may be handed out through that there and students may discuss about there problem.
Learning outcomes
After completion of the course the student is mastering the topological foundations of the functional analysis 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 theoryY Rieszin representaion theorem | The proofs involving results connecting Lebesgue and the generalized measure theory | The proof of the Riesz represention theorem |
| 3. | Distirbution theory and its applications to partial differential equations | The exact definition of the distribution space topology | |
| 4. | Sobolev spaces |
Evaluation criteria for the course
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 | English | ||||
| Book | Functional Analysis | Lax | English | ||||
| Book | Functional Analysis | Rudin | English | ||||
| Summary of lectures | MAT-53550 Advanced Functional Analysis | Eriksson | English |
Prerequisites
| Course | Mandatory/Advisable | Description |
| MAT-41140 Johdatus funktionaalianalyysiin | Advisable | |
| MAT-41146 Introduction to Functional Analysis | Advisable | |
| MAT-41291 Mitta- ja integraaliteoria | Advisable | |
| MAT-41297 Measure and Integral Theory | Advisable | |
| MAT-43850 Matemaattinen analyysi 2 | 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 |