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

approximate amount of contact lessons

56

Teaching semester

autumn

Assessment form

Examination

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.

Teacher

dots M.Väljas

Prerequisite course 1

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.

Lumiste, Ü. 1987 Diferentsiaalgeomeetria. Tallinn: Valgus;

Gray, A. 1998 Modern differential geometry of Curves and Surfaces with Mathematica. USA : CRC Press LLC.