FYNCTIONAL ANALYSIS
| Title | ΣΥΝΑΡΤΗΣΙΑΚΗ ΑΝΑΛΥΣΗ / FYNCTIONAL ANALYSIS |
| Code | Θ027 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Georgios Sakellaris |
| Common | Yes |
| Status | Active |
| Course ID | 600025916 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2025-2030)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| THEŌRĪTIKA MATHĪMATIKA | Elective Courses belonging to the selected specialization | Spring | - | 10 |
| Academic Year | 2025 – 2026 |
| Class Period | Spring |
| Faculty Instructors | |
| Weekly Hours | 3 |
| Total Hours | 39 |
| Class ID | 600268426
|
Course Type 2021
Specialization / Direction
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600268426
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
Prerequisites
General Prerequisites
Calculus, Topology of metric spaces, Functional Analysis (undegraduate).
General Competences
- Apply knowledge in practice
- Retrieve, analyse and synthesise data and information, with the use of necessary technologies
- Work autonomously
Course Content (Syllabus)
i) Banach spaces, dual spaces, finite dimensional spaces.
ii) The basic theorems: the uniform boundedness principle, the open mapping theorem, the closed graph theorem. The Hahn-Banach theorem, applications to functionals.
iii) Hilbert spaces. The Riesz theorem, projecctions. The theorems of Stampacchia and Lax-Milgram.
iv) Weak and weak* topologies. The theorems of Banach-Alaoglou, Mazur, Goldstine.
v) Reflexive spaces.
vi) Compact operators. The Fredholm alternative, the spectral theorem for selfadjoint compact operators.
vii) Topological vector spaces, locally convex spaces. Applications of the Hahn-Banach theorem, the Krein-Milman theorem.
Educational Material Types
- Notes
- Book
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | ||||
| Reading Assigment | 234 | ||||
| Written assigments | 24 | ||||
| Exams | 3 | ||||
| Total | 300 |
Student Assessment
Student Assessment methods
- Written Exam with Multiple Choice Questions (Formative, Summative)
- Written Exam with Short Answer Questions (Formative, Summative)
- Written Exam with Extended Answer Questions (Formative, Summative)
- Written Assignment (Formative, Summative)
- Oral Exams (Formative, Summative)
- Performance / Staging (Formative, Summative)
- Written Exam with Problem Solving (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
- Functional Analysis, Sobolev Spaces and Partial Differential Equations, του Haim Brezis
- A course in Functional Analysis, του John Conway
- Σημειώσεις Μεταπτυχιακής Ανάλυσης ΙΙ, του Απόστολου Γιαννόπουλου.
Last Update
30-11-2024
