PARTIAL DIFFERENTIAL EQUATIONS
| Title | ΔΙΑΦΟΡΙΚΕΣ ΕΞΙΣΩΣΕΙΣ ΜΕ ΜΕΡΙΚΕΣ ΠΑΡΑΓΩΓΟΥΣ / PARTIAL DIFFERENTIAL EQUATIONS |
| Code | Θ024 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Georgios Sakellaris |
| Common | Yes |
| Status | Active |
| Course ID | 600025913 |
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 | 600268423
|
Course Type 2021
Specialization / Direction
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600268423
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.
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) Introductory material from Functional Analysis: weak topologies, weak convergence, weak compactness.
ii) Sobolev spaces: Definitions, approximations, extensions, traces. The Gagliardo-Nirenberg-Sobolev inequality, the Morrey estimate, general Sobolev inequalities. Compactness, Poincare inequalities, differnce quotients. Dual spaces.
iii) Second order elliptic equations: weak solutions, the Lax-Milgram theorem, energy estimates. Smoothness, maximum principle, eigenvalues and eigenvectors.
iv) Second order parabolic equations: weak solutions, the Galerkin method, smoothness, maximum principle.
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
Description
Graded homeworks, and either a final exam, or evaluation of presentations.
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)
-Partial Differential Equations: Second Edition (Graduate Studies in Mathematics), του Lawrence Evans
-Functional Analysis, Sobolev Spaces and Partial Differential Equations, του Haim Brezis
Last Update
30-11-2024
