| Area of Mathematics: | Algebra and Geometry | ||
| Semester: | 5ο | ||
| Course ID: | 51201 | ||
| Course Type: | Compulsory | ||
| Teaching hours per week: | Theory: 4 | Practice: 1 | Laboratory: 0 |
| ECTS : | 6 | ||
| Eclass: | For the course’s material, click here. | ||
| Instructors: | Statha Marina | ||
Description
- Plane and space curves, tangent line of regular curve, arclength, parametrization by arclength (physical parameter), Frenet frame, curvature and torsion, generalized helix, fundamental theorem of curves, the isoperimetric inequality.
- Regular surfaces, differentiation of maps between surfaces, tangent plane, first and second fundamental form, surface area, isometries, Gauss map, shape operator (Weingarten map), normal curvature, principal curvatures, Gauss curvature, mean curvature, Theorema Egregium, geodesics, Clairaut theorem, Gauss-Bonnet theorem.
Bibliography
- O’ Neil B. Elementary Differential Geometry, Revised 2nd Edition
- Pressley A. N. Elementary Differential Geometry, Springer Undergraduate Mathematic Series.
- Manfredo P. do Carmo Differential Geometry of Curves and Surfaces: Revised and Updated Edition (Dover Books on Mathematics).
