Course title in Estonian
Course title in English
approximate amount of contact lessons
lecturer of 2019/2020 Spring semester
õppejõud on määramata
lecturer of 2020/2021 Autumn semester
lecturer not assigned
The goal of the subject is to provide an overview of spaces used in geometry. The use of various methods of analytic geometry. The mathematical theory of quadratic curves.
Brief description of the course
Concepts of affine space and Euclidean space. The main problems of analytic geometry. The concepts of pencil and bundle of lines, circles, and planes, applications. Conic sections. Polar equations of conic sections. General equations of second order curves. The simplification of general equations with shift of frame and rotation of frame. Invariance of second order curves. Conjugate diameters and directions, asymptotic directions and main directions of second order curves. Tangents of second order curves. The simplification of general equations of second order curves and the eigenvalue problem.
(approximately 48 academic hours) consists of working with the study literature, lecture notes and solving the exercises.
Learning outcomes in the course
After passing this course the student
- knows main notions of analytical geometry;
- is familiar with the main properties, relations and teorems taught in this course;
- is able to solve standard exercises and problems of analytical geometry.
Examination. Two written practical tests must be done before the final theoretical examination.
The course is a prerequisite
Bazõlev, V.; Dunitsev, K. 1974 Geometria I (vene keeles). Moskva: Prosveštšenie.