Differential Manifolds
| Title | ΔΙΑΦΟΡΙΣΙΜΕΣ ΠΟΛΛΑΠΛΟΤΗΤΕΣ / Differential Manifolds |
| Code | 0304Α |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Winter |
| Common | No |
| Status | Active |
| Course ID | 600019939 |
Programme of Study: Merikīs Foítīsīs (2014-sīmera)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| KORMOS | Elective Courses belonging to the selected specialization | Winter | - | 5.5 |
Programme of Study: UPS of School of Mathematics (2014-today)
Registered students: 41
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Elective Courses belonging to the selected specialization | 7 | 4 | 5.5 |
| Academic Year | 2025 – 2026 |
| Class Period | Winter |
| Faculty Instructors |
|
| Weekly Hours | 3 |
| Total Hours | 39 |
| Class ID | 600276099
|
Course Type 2021
Specialization / Direction
Course Type 2011-2015
Knowledge Deepening / Consolidation
Mode of Delivery
- Face to face
- Distance learning
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600276099
- At the Website of the School:
- eLearning: https://elearning.auth.gr/course/view.php?id=7897
- eLearning (Moodle):
Language of Instruction
- Greek (Instruction, Examination)
Prerequisites
Required Courses
- 0201 Calculus I
- 0233 General Topology
- 0110 ELEMENTS OF LINEAR ALGEBRA
- 0305 ELEMENTS OF ANALYTIC GEOMETRY
- 0306 INTRODUCTION TO GEOMETRY I
- 0108Α Linear Algebra
- 0202Α Calculus II
- 0203Α Calculus III
- 0204Α Topology of Metric Spaces
- 0205Α Calculus IV
- 0206Α Differential Equations
General Competences
- Work autonomously
- Work in teams
- Work in an international context
- Work in an interdisciplinary team
- Generate new research ideas
Course Content (Syllabus)
Homeomorphic topological spaces. Topological manifolds. The notion of differentiable manifold, construction and examples of differentiable manifolds. Maps between manifolds. Submanifolds. Tangent vectors, tangent space and tangent vector bundle. Vector fields and Lie bracket. Covectors, cotangent space and cotangent bundle. Forms. The differential of a map, pushforward and pullback.
Keywords
Manifolds
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
- Use of ICT in Student Assessment
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 110 | ||||
| Reading Assigment | 52 | ||||
| Written assigments | |||||
| Exams | 3 | ||||
| Total | 165 |
Student Assessment
Description
Home work - Γραπτή Εργασία
Student Assessment methods
- Written Exam with Extended Answer Questions (Formative, Summative)
- Written Assignment (Formative, Summative)
- Oral Exams (Formative, Summative)
- Written Exam with Problem Solving (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
- Διαφορικές Μορφές, Manfredo Do Carmo, Leader Books, 2010
- Γεωμετρία Πολλαπλοτήτων, Πολλαπλότητες Riemann και Ομάδες Lie, http://hdl.handle.net/11419/146
Additional bibliography for study
1. Δημητρίου Κουτρουφιώτη, Διαφορική Γεωμετρία, Πανεπιστήμιο Ιωαννίνων 1994.
2. Loring W. Tu, An introduction to Manifolds, Universitext, Springer 2011.
3. John M. Lee, Introduction to Smooth Manifolds, GTM 218, Springer 2003.
4. Gadea, Pedro M., Muñoz Masqué, Jaime, Mykytyuk, Ihor V., Analysis and Algebra on Differentiable Manifolds A Workbook
for Students and Teachers, Published 2013
https://link.springer.com/book/10.1007/978-94-007-5952-7
5. Lafontaine, Jacques, An Introduction to Differential Manifolds
Published 2015
https://link.springer.com/book/10.1007/978-3-319-20735-3
6. Gross, Gal, Meinrenken, Eckhard: Manifolds, Vector Fields, and Differential Forms An Introduction to Differential Geometry
Published 2023
https://link.springer.com/book/10.1007/978-3-031-25409-3
Last Update
01-10-2025
