Differential Geometry
Course code
MLM7214.DT
old course code
MLM7214
Course title in Estonian
Diferentsiaalgeomeetria
Course title in English
Differential Geometry
ECTS credits
5.0
Assessment form
Examination
lecturer of 2024/2025 Autumn semester
Not opened for teaching. Click the study programme link below to see the nominal division schedule.
lecturer of 2024/2025 Spring semester
Not opened for teaching. Click the study programme link below to see the nominal division schedule.
Course aims
Major. Mathematically modelling lines and surfaces in space. Introducing differential geometrical characteristics of submanifolds and applying them. Introducing the main concepts of differential geometry and their applications. Using modern computing technology for solving problems in differential geometry.
Brief description of the course
Vector function of scalar variables. Equations of a smooth line. Tangential line, normal and bending plane of line. Moving frame. The Bartels-Frenet formulas. The curvature and twist of a line. Circle of curvature, evolute and evolvent. Equations of smooth surface, tangent plane and normal line for surface. First and second fundamental form, metrical quantities on the surface. Normal curvature of the line. Principal directions of the surface and curvature lines on the surface. Asymptotical directions and lines of the surface. Geodesic curvature of the line and geodesic lines on the surface. Gauss and Gauss-Bonnet theorems. Inner geometry of surfaces with a constant main curvature. Main theorem of surface theory.
Learning outcomes in the course
Upon completing the course the student:
Knows mathematical facts and is able to use methods in volume of the subject.
Knows mathematical facts and is able to use methods in volume of the subject.
Teacher
dots M.Väljas
Prerequisite course 1
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