Analytical Geometry
Course code
MLM6204.DT
old course code
MLM6204
Course title in Estonian
Analüütiline geomeetria
Course title in English
Analytical Geometry
ECTS credits
4.0
approximate amount of contact lessons
56
Teaching semester
autumn
Assessment form
Examination
lecturer of 2020/2021  Autumn semester
õppejõud on määramata
lecturer of 2020/2021  Spring semester
lecturer not assigned
Course aims
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.
Independent work
(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.


Assessment methods
Examination. Two written practical tests must be done before the final theoretical examination.
Teacher
lekt Tõnu Tõnso
Prerequisite course 1
Replacement literature
Bazõlev, V.; Dunitsev, K. 1974 Geometria I (vene keeles). Moskva: Prosveštšenie.