Differential Geometry
Course code
MLM6407.DT
old course code
Course title in Estonian
Diferentsiaalgeomeetria
Course title in English
Differential Geometry
ECTS credits
6.0
Assessment form
Examination
lecturer of 2023/2024 Spring semester
Not opened for teaching. Click the study programme link below to see the nominal division schedule.
lecturer of 2024/2025 Autumn semester
Not opened for teaching. Click the study programme link below to see the nominal division schedule.
Course aims
To teach students to model curves and surfaces of the three-dimensional space mathematically. To introduce the main differential geometric characteristics of manifolds and to teach the application process of those characteristics. To introduce main notions of differential geometry with their applications. To use modern computer technology for solving the exercises in differential geometry.
Brief description of the course
Vector-valued function of scalar variable. Equations of a smooth curve. Tangent of a curve, normal plane and osculating plane. Moving frame of a curve, Bartels-Frenet-Serret formulae. Curvature and torsion of a curve. Osculating circle, evolutes and evolvents. The notion and equations of a surface, tangent plane and normal. First fundamental form of a surface, metric magnitudes on the surface. Second fundamental form of a surface. Normal curvature of a surface. General directions of surfaces and lines of curvature. Asymptotic directions of a surface and asymptotic curves. Geodetic curvature of a curve, geodetic lines. Theorem of Gauss. Theorem of Gauss-Bonnet. Intrinsic geometry of surfaces of constant curvature. The fundamental theorem of surfaces.
Learning outcomes in the course
Upon completing the course the student:
- knows the mathematical facts and methods introduced in the lectures, is able to justify and apply them
- knows the mathematical facts and methods introduced in the lectures, is able to justify and apply them
Teacher
lekt Mati Väljas
Prerequisite course 1
Study programmes containing that course