-Intoduction to vector calulus. Sum and difference of two vectors. Exterior product of a vector. Algebraic form of a vector. Inner product of vectors.
-Structure of vector spaces: Basic algabraic structures. Vector spaces. Vector subspaces.
-Linear dependence and bases: Linear combination of vectors. Linear dependence and indendence. ?Basis and dimension of a vector space.
-Representation of vectors and geometric concepts: Coordinates of a point in orthogonal and oblique systems. Projection of a vector. Direction cosines. Exterior and mixed product of vecors.
-Matrices and properties: Definition of a matrix. Operations of matrices. Symmetric,antisymmetric and orthogonal matrices. Powers of matrices. Comlex matrices. Inner product of real and comlex vectors.
-Determinants and inverse matrices. Properties of determinats. Evaluation of a determinant. Inverse matrix with the use of determinants.
-Transformation of matrices. Elementary transformations. Stepped matrices. Rank of a matrix. Nonhomogeneous and homogeneous linear systems.
-Methods of solving linear systems: Gauss elimination. Cramer method. Inverse matrix method. Linear system investigation.
-Einvalues and eigenvectors: Definitions and properties. Their calculation. Cayley–Hamilton theorem. Similar matrices and similarity transformations. Diagonalization of matrices. Minimal polynomial of a matrix.
-Changa of basis in Eucledian space. Coordinates in Eucledian space. Transposition and rotation of the axes. Cartesian, polar, cylidrical and spherical coordinate system.
-Staight lines and planes in Eucledian space.: Equations of straight lines and planes. Comparative position of straight lines and planes.
-Conic sections, circle, parabola, Ellipse, Hyperbola. Definitions and properties.