Overview
Aims
Introducing basic concepts and methods of numerical analysis.
Initiating students in methods of numerical programming for solving mathematical problems and for start using numerical software. Students have to know the fundamental concepts of numerical analysisand various numerical algorithms.
These specific objectives allow modeling and solving complex problems using knowledge of mathematics and informatics.
Course contents
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
Learning outcomes
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.
Assessment
Final evaluation – 50%; Laboratory activities – 50%.