NUMERICAL CALCULUS

1. Elements of approximation theory and matrix analysis 1.1 Analysis and evaluation of arithmetic expressions 1.2 Items of errors theory and floating point arithmetic 1.3 Calculating the determinant and inverse of a matrix 2. Methods and numerical algorithms. Differences calculus 2.1 Gauss elimination method 2.2 Total elimination method 3. Functions approximations 3.1 Cholesky method 3.2 Onicescu method 3.3 Iterative methods 3.4 Successive approximations method 3.5 Tangent method 3.6 Secant method 4. Numerical differention and integration algorithms 4.1 Bairstrov method 4.2 Finite differences methods 4.3 Divided differences methods 5. Numerical algorithms for solving algebraic equations 5.1 Approximation in mean square 5.2 Numerical differentiation 6. Items of Symbolic Calculus 6.1 Quadrature formulas of Gauss and Newton Cotes type 6.2 Numerical integration using Taylor series 6.3 Multipas methods

In order to obtain credits for this discipline, the students have to operate with elementary items of numerical analysis and use soft for solving different mathematical problems.