Functional Analysis
| Title | ΣΤΟΙΧΕΙΑ ΣΥΝΑΡΤΗΣΙΑΚΗΣ ΑΝΑΛΥΣΗΣ / Functional Analysis |
| Code | 0232 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Spring |
| Common | No |
| Status | Active |
| Course ID | 40000498 |
Programme of Study: UPS of School of Mathematics (2014-today)
Registered students: 92
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Elective Courses belonging to the selected specialization | Spring | - | 5.5 |
| Academic Year | 2023 – 2024 |
| Class Period | Spring |
| Faculty Instructors |
|
| Weekly Hours | 3 |
| Class ID | 600230618
|
Course Type 2016-2020
- Scientific Area
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600230618
- eLearning: https://elearning.auth.gr/course/view.php?id=17427
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
- English (Examination)
Prerequisites
Required Courses
- 0207 Introduction to Real Analysis
- 0204Α Topology of Metric Spaces
General Competences
- Apply knowledge in practice
- Adapt to new situations
- Advance free, creative and causative thinking
Course Content (Syllabus)
Metric topology recap, complete metric spaces. Vector spaces, Hamel basis. Normed spaces, Banach spaces, finite-dimensional spaces. Linear operators and functionals, norms of bounded operators. Inner product spaces, Hilbert spaces, orthonormal basis, Schauder basis, Riesz representation theorem. Hahn-Banach theorem, open mapping theorem, closed graph theorem.
Educational Material Types
- Notes
- Book
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Course Teaching
- Use of ICT in Communication with Students
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | 1.3 | |||
| Reading Assigment | 123 | 4.1 | |||
| Exams | 3 | 0.1 | |||
| Total | 165 | 5.5 |
Student Assessment
Student Assessment methods
- Written Exam with Extended Answer Questions (Formative, Summative)
- Written Exam with Problem Solving (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
- Στοιχεία Συναρτησιακής Ανάλυσης, Χ. Καρυοφύλλης, Εκδ. Ζήτη, 1995
- Γενική Τοπολογία και Συναρτησιακή Ανάλυση, Σ. Νεγρεπόντης- Θ. Ζαχαριάδης-Ν. Καλαμίδας-Β. Φαρμάκη,
Εκδ. Αθανασόπουλος,1997
- Συναρτησιακή Ανάλυση, Haim Brezis, Εκδ. ΕΜΠ, 1997
Last Update
10-02-2023
