Infopaket

General algebra

ОК.13

Обов’язкова дисципліна для ОП

First

2023/2024

2 Semester

4

As a result of studying the course the student will gain basic theoretical concepts and practical skills in analytical geometry, higher and linear algebra.

Full-time form

The student must have a high knowledge of mathematics in the secondary school program

Module I. Space of geometric vectors, bases and coordinates. Scalar, vector and mixed multiplication vectors. Plane in space and its equations. The distance from the point to the plane. line in space and its equations. Basic curves of the second order and their focal properties. Module II. Matrices and operations with them. Determinant of a square matrix and methods of its calculation. Inverse matrix. Matrix equations. Matrix rank, base minor. Systems of linear equations: Kronecker-Capelli criterion, basic methods of solution. Solution space and structure of the general solution of a system of linear homogeneous equations. Module III. Vector space (general questions). Base replacement. Linear shell vectors, vector subspaces. Euclidean spaces. Linear mappings and linear operators. Eigenvalues and vectors of a linear operator. Linear mappings in Euclidean and unitary spaces.

1. Алгебра. Методичний посібник для практичних занять студентів радіофізичного факультету університету. / С.В.Єфіменко, Т.М. Жеребко – К.: КНУ, 2014 – 123 с– К.: КНУ, 2014 – 123 с 2. Завало С.Т. Курс алгебри – К.: Вища школа, – 1988, 502 с. 3. Зайцева Л.Л., Нетреба А.В. Аналітична геометрія в прикладах і задачах. – Київ: Видавничополіграфічний центр «Київський університет», 2008. – 200 с. 4. Калужнін Л. А. Лінійні простори //Л. А. Калужнін, В. А. Вишенський, Ц. О. Шуб. – К.: Вища школа,1971. – 343 с. 5. Придатченко Ю.В., Вільчинський С.Й., Львов В.А. Лінійна алгебра для фізиків. – Київ: Київський університет, 2010. – 159 с.

Lectures, practical training, self-dependent work of students

The grade for studying the course consists of grades for self-dependent work (up to 30 points), test tasks (up to 30 points) and grades for the exam (up to 40 points).

Ukrainian