MMG0004 | Geometry 3 (Curves and Surfaces) |
Teaching Staff in Charge |
Lect. VACARETU Daniel, Ph.D., vacaretumath.ubbcluj.ro Prof. VARGA Csaba Gyorgy, Ph.D., csvargacs.ubbcluj.ro |
Aims |
The course gives to the students the principal tools and also the necesary methods in the study of curves and surfaces with an accent on the intuitive side. |
Content |
I. Local theory of curves.
1. Curves in euclidean space.Tangent line and normal plane. 2. Curves in general position. Osculating plane. 3. Frenet frame. Frenet formulas. Curvature and torsion. 4. Geometric iterpretation of curvature and torsion. 5. Contact beatween two curves. 6. Evolute and involute. 7. Envelope of a family of curves in plane. II.Local theory of surfaces. 1. Surfaces in three-dimensional euclidean space. 2. Tangent plane and normal line of a surface. 3. First fundamental form of a surface. 4. Arc length , angle between two curves on surface .Area element. 5. Second fundamental form. 6. Normal curvature. 7. Asymptotic lines of a surface. 8. Principal curvatutres of a surface. Mean curvature and Gaussian curvature. 9. Theorema egregium. 10.Minimal surfaces and surfaces with constant curvature. 11.Darboux frame. Darboux formulas. 12.Geodesic curvature. Geodesic torsion. 13.Geodesic lines. |
References |
1. BLAGA A. PAUL, Lectures on Classical Differential Geometry, Ed.
RISOPRINT, Cluj-Napoca, 2005 2. DOBRESCU A., Curs de Geometrie Diferentţială, Ed. Didactică şi Pedagogică, Bucureşti, 1963 3. ENGHIŞ P., ŢARINĂ M., Curs de Geometrie Diferenţială, Cluj-Napoca, 1985 4. FINIKOV P.S., Curs de Geometrie Diferenţială, Ed. Tehnica, Bucureşti, 1954 5. MURGULESCU E., col., Geometrie analitică şi diferenţială, Editura Didactică şi Pedagogică, Bucureşti, 1965. 6. MURGULESCU E., col., Culegere de probleme de geometrie analitică şi diferenţială, vol.1 Ed. Didactică şi Pedagogică, Bucureşti, 1971 7. MURGULESCU E., col., Geometrie analitică in spatiu şi geometrie diferenţială, Culegere de probleme, vol. 2 Ed. Didactică şi Pedagogică, Bucureşti. 8. PINTEA C., Geometrie, Presa Universitară Clujeană, 2001. 9.TEODORESCU I.D., Geometrie Superioara, Ed. Didactică şi Pedagogică, Bucureşti , 1970 10.TEODORESCU I.D., TEODORESCU S.D., Culegere de probleme de Geometrie Superioara, Ed. Didactică şi Pedagogică, Bucureşti, 1975 |
Assessment |
Final exam + 2 assessement tests + homework
|
Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |