Elementary Differential Geometry (MAY522)
Undergraduate Courses Outlines - Department of Mathematics
General
| School |
School of Science |
|---|---|
| Academic Unit |
Department of Mathematics |
| Level of Studies |
Undergraduate |
| Course Code |
MAY522 |
| Semester | 5 |
| Course Title |
Elementary differential geometry |
| Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 5, Credits: 7.5) |
| Course Type |
General Background |
| Prerequisite Courses | - |
| Language of Instruction and Examinations |
Greek |
| Is the Course Offered to Erasmus Students |
Yes (in English) |
| Course Website (URL) |
Learning Outcomes
| Learning outcomes |
It is an introductory course on differential geometry. The aim is to introduce and study geometric properties of regular curves (both plane and space) and regular surfaces. Fundamental notions of differential geometry of curves and surfaces are introduced and studied. Among them is the notion of curvature. The study requires tools from Linear Algebra and Calculus of several variables.
|
|---|---|
| General Competences |
|
Syllabus
- Plane curves, arclength, curvature, Frenet frame.
- Space curves, curvature and torsion, Frenet frame, fundamental theorem of curves.
- Surfaces, parametrization, Gauss map, Weingarten map, first and second fundamental form, normal curvature, principal and asymptotic directions, Gaussian and mean curvature, minimal surfaces, Theorema Egregium, Gauss and Weingarten formulas, fundamental theorem of surfaces, developable surfaces.
Teaching and Learning Methods - Evaluation
| Delivery |
Direct | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology | - | ||||||||
| Teaching Methods |
| ||||||||
| Student Performance Evaluation |
Written final examination |
Attached Bibliography
- Δ. Κουτρουφιώτης, Στοιχειώδης Διαφορική Γεωμετρία, Εκδόσεις Leader Books, 2006
- Barrett O' Neil, Στοιχειώδης Διαφορική Γεωμετρία, Πανεπιστημιακές Εκδόσεις Κρήτης, 2002
- Andrew Pressley, Στοιχειώδης Διαφορική Γεωμετρία, Πανεπιστημιακές Εκδόσεις Κρήτης, 2011
- Manfredo do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, 1976