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 2019/2020 Spring semester

õppejõud on määramata

lecturer of 2020/2021 Autumn 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.

- 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

The course is a prerequisite

Replacement literature

Bazõlev, V.; Dunitsev, K. 1974 Geometria I (vene keeles). Moskva: Prosveštšenie.