Преподавател(и):

проф. Иван Ланджев  д.н.

Описание на курса:

Компетенции:

Students will learn:

How to apply Gaussian elimination for solving homogeneous and non-homogeneous linear systems of equations;

How to present in different forms the general solution of a system of linear equations;

To give geometrical interpretation of the set of all solutions to a system of equations;

To work with matrices, to represent a matrix as a product of a lower-triangular and upper-triangular matrix;

To calculate the inverse of a given matrix;

To find the Rank of a matrix, the dimension of a given vector space and to provide a basis for it;

To calculate determinants;

To find Eigen-Values and Eigen-Vectors of square matrices.

Предварителни изисквания:

Elementary mathematics (school level);

Desire for self-standing work on Home-works and Assignments given during classes.

Форми на провеждане:
Редовен

Учебни форми:
Самостоятелна работа

Език, на който се води курса:
Английски

Теми, които се разглеждат в курса:

The assignments given to students cover (and are related to) the topics considered in NETB103 Linear Algebra:

Solving systems of linear equations (homogeneous and non-homogeneous) by Gaussian Elimination;

Representing in different forms the general solution of a system of linear equations;

Vectors and matrices; Product of matrix and a vector, product of two matrices; Representation of Gaussian elimination steps as a sequence of multiplication of a matrix by elementary matrices; Permutations of matrix rows as multiplication of matrices; Representation of a matrix as a product of two matrices: a lower-triangular one and an upper-triangular one;

Methods for calculation of Inverse matrices;

Rang of a matrix; Dimension and basis of a vector space;

Vector spaces generated by a matrix;

Scalar (inner) product of two vectors;

Orthogonality of vectors and subspaces;

Determinants and their applications;

Eigen-Values and Eigen-Vectors of square matrices.

Литература по темите:

Any of the numerous text-books on Linear Algebra and its applications could be of help.

Preferred book:

Gilbert Strang, "Linear Algebra and itsw Applications",

Brooks/Cole, Third Edition,

ISBN 0-15-551005-3

Средства за оценяване:

The final mark (from 2 to 6) takes into account:

The quality and the number of solved Assignments as well as

the regularity of their presentation to the teacher;

The marks from the two written Control works during the term;

The mark from the written Final Exam at the end of the term