Classical Differential Geometry II
| Title | ΚΛΑΣΙΚΗ ΔΙΑΦΟΡΙΚΗ ΓΕΩΜΕΤΡΙΑ ΙΙ / Classical Differential Geometry II |
| Code | 0332 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Spring |
| Common | Yes |
| Status | Active |
| Course ID | 40000470 |
Programme of Study: UPS of School of Mathematics (2014-today)
Registered students: 18
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Elective Courses belonging to the selected specialization | Spring | - | 5.5 |
| Academic Year | 2018 – 2019 |
| Class Period | Spring |
| Faculty Instructors |
|
| Weekly Hours | 3 |
| Class ID | 600121487
|
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/1/600121487
- Other: http://stamata.webpages.auth.gr/geometry/
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
- English (Instruction, Examination)
- French (Instruction, Examination)
- German (Instruction, Examination)
Prerequisites
Required Courses
- 0301 Analytic Geometry I
- 0302 Analytic Geometry II
- 0303 Classical Differential Geometry I
Learning Outcomes
Introduction, deeping and understanding of advanced topics in Differential Geometry
General Competences
- Apply knowledge in practice
- Make decisions
- Work autonomously
- Work in teams
- Work in an international context
- Work in an interdisciplinary team
- Generate new research ideas
- Advance free, creative and causative thinking
Course Content (Syllabus)
The moving frame of G. Darboux. Inner Differential Geometry. The formula of Gauss-Bonnet and its applications. The method of E. Cartan. The formula of Euler. Dupin's indicantrix. Conjugate directions. Parallel surfaces. Integral formulae of H. Schwarz and H. Minkowski, Theorem by E. Rembs - W. Süss.
Keywords
Darboux-moving frame, inner Differential Geometry, Formula of Gauss-Bonnet, Cartan's method, Euler's formula, Dupin's indicatrix, parallel surfaces, integral formulae
Educational Material Types
- Notes
- Book
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Communication with Students
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 130 | 4.3 | ✓ | ✓ | |
| Reading Assigment | 15 | 0.5 | ✓ | ✓ | ✓ |
| Tutorial | 18 | 0.6 | ✓ | ✓ | ✓ |
| Exams | 3 | 0.1 | ✓ | ✓ | ✓ |
| Total | 166 | 5.5 |
Student Assessment
Description
Written examination
Student Assessment methods
- Written Exam with Multiple Choice Questions (Summative)
- Written Exam with Short Answer Questions (Summative)
- Written Exam with Extended Answer Questions (Summative)
- Written Assignment (Summative)
- Written Exam with Problem Solving (Summative)
Bibliography
Course Bibliography (Eudoxus)
- Σ. Σταματάκη: Εισαγωγή στην Κλασική Διαφορική Γεωμετρία, Θεσσαλονίκη, Εκδόσεις Αϊβάζη, 2008
- Ν. Στεφανίδη: Διαφορική Γεωμετρία, Β’ έκδοση βελτ. και επαυξ. Θεσσαλονίκη, 2014
- A. Pressley: Στοιχειώδης Διαφορική Γεωμετρία.Ηράκλειο : Πανεπιστημιακές Εκδόσεις Κρήτης, 2011
- B. O'Neill: Στοιχειώδης Διαφορική Γεωμετρία, Ηράκλειο : Πανεπιστημιακές Εκδόσεις Κρήτης, 2002
- Δ. Κουτρουφιώτη: Στοιχειώδης διαφορική γεωμετρία, Αθήνα : Leader Books, 2006
Additional bibliography for study
- M. P. do Carmo: Differential Geometry of Curves and Surfaces. Prentice – Hall, 1976
- O. Giering and J. Hoschek: Geometrie und ihre Anwendungen. Carl Heuser Verlag, 1994
- A. Gray: Modern Differential Geometry of Curves and Surfaces with Mathematica. Second edition. CRC Press, 1998
- W. Haack W.: Elementare Differentialgeometrie. Birkhäuser Verlag, 1955
- C. C. Hsiung: A first Course in Differential Geometry. John Wiley & Sons, 1981
- Kreyszig E.: Differential Geometry. University of Toronto Press, 1959
- Laugwitz D.: Differentialgeometrie. B.G.Teubner, 1977
- J. Lelong-Ferrand, J. M. Arnaudiés: Cours de Mathématiques. Tome 3, Géometrie et cinématique. Dunod, 1977
- J. Oprea: Differential Geometry and its Applications. Prentice Hall, 1997
- Β. Παπαντωνίου: Διαφορική Γεωμετρία, Πάτρα : Εκδόσεις Πανεπιστημίου Πατρών, 1996- 1997
- G. Στάμου: Ασκήσεις Διαφορικής Γεωμετρίας. Εκδόσεις Ζήτη, 1990
- G. Scheffers: Anwendung der Differential- und Integralrechnung auf Geometrie. W. d. Gruyter & Co, 1922
Last Update
17-05-2019
