MATHEMATICAL ANALYSIS I

Sequences of real numbers, convergence tests. Series of real numbers, convergence tests. Functions of real numbers. Trigonometrical functions. Hyperbolic functions. Continuous functions. Derivatives of functions. Fundamental theorems. Power series. Taylor and Maclaurin series. The Riemann integral of a real-valued function. Applications. Generalized integrals. Applications.

LINEAR ALGEBRA

Vector calculus, lines and planes in 3-space. The basic surfaces. Matrices, determinants and linear systems. Linear spaces (introduction, linear subspace, linear independence, basic, dimension, sum of subspaces). Linear mappings (basic definitions, the matrix of a linear mapping, the basic geometric transformations, change of basis). Eigenvalues and eigenvectors of linear transformations and matrices (characteristic polynomial, Cayley-Hamilton theorem, matix diagonalization). Orthogonal and symmetric matrices.