Differential Geometry
Course code
old course code
Course title in Estonian
Course title in English
Differential Geometry
ECTS credits
approximate amount of contact lessons
Teaching semester
Assessment form
lecturer of 2019/2020  Spring semester
õppejõud on määramata
lecturer of 2020/2021  Autumn semester
lecturer not assigned
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.
Independent work
Homework based on lecture materials, literature and problem solving. Two individual home-tests which require working in computer class. Preparations for classroom tests and final examination.
Learning outcomes in the course
Knows mathematical facts and is able to use methods in volume of the subject.
Assessment methods
Executing two test papers and presenting two homework assignments executed in computer class is a prerequisite for sitting the examination. The examination contains two theoretical questions and one practical exercise.
dots M.Väljas
Study literature
Lumiste, Ü. 1963 Diferentsiaalgeomeetria Tallinn: Valgus;
Lumiste, Ü. 1987 Diferentsiaalgeomeetria. Tallinn: Valgus;
Gray, A. 1998 Modern differential geometry of Curves and Surfaces with Mathematica. USA : CRC Press LLC.