1. 
Course title 
Numerical methods 
2. 
Course of Study, Speciality 
4, 131 03 01 Mathematics (majors in) Major in 131 03 0101 Mathematics (Research Activities and Production) 
3. 
Semester

7 
4. 
Credits 
3 
5. 
Lecturer 
Azarov Alexey Ivanovich Candidate of Physical and Mathematical Sciences, Associate Professor 
6. 
Course goal 
– construction of mathematical models, determination of their role and significance; – familiarity with the basic principles of developing computational methods for typical and new mathematical models; – study and development of the theory and applications of computing methods, their computer implementations; – analysis of the reliability of numerical results, their interpretation and implementation. 
7. 
Prerequisites 
– algebra and number theory; – Geometry, mathematical analysis; – modern systems of computer modeling – differential equations; – equations of mathematical physics; – integral equations; – Mechanics 
8. 
Course Topics 
Numerical methods for solving LAA systems. Norms of vectors and matrices. Estimation of the error in the solution of the LAA systems. Direct methods. The Gauss method. Calculation of eigenvalues and eigenvectors of matrices. Properties of eigenvectors and eigenvalues of matrices. Converting similarity. The Danilevsky method. Solution of nonlinear equations and systems. Separation of roots. Method of dichotomy. Multiple roots. The roots of polynomials. Simple iteration method. The convergence condition and the rate of convergence. Newton’s method. Numerical solution of the Cauchy problem for ordinary differential equations. Onestep methods. Euler’s method. Estimate of the rate of convergence. RungeKutta methods. Multistep methods. Numerical solution of boundary value problems for ordinary differential equations. Difference method for solving a boundaryvalue problem for a secondorder equation. Methods for constructing difference schemes. Integrointerpolation method. The concept of compact difference schemes. Galerkin’s method. Approximation and convergence. Numerical solution of Fredholm integral equations. Basic approaches to solving integral equations. The Fourier method for the numerical solution of integral equations of convolution type. Construction and investigation of difference schemes for problems of mathematical physics. Difference schemes for the heat equation. The canonical form and the stability condition for twolayer difference schemes. Stability, approximation and convergence. Difference schemes for the transport equation. Spectral criterion of stability. Difference schemes for elliptic equations. The maximum principle 
9. 
Recommended Literature 
1. Бахвалов Н.С., Жидков Н.П., Кобельков Г.М. Численные методы. – М.: Наука, 1987. 2. Крылов В.И., Бобков В.В., Монастырный П.И. Вычислительные методы высшей математики. В 2 т. – Минск: Выш. шк., 1972, 1975. 3. Крылов В.И., Бобков В.В., Монастырный П.И. Начала теории вычислительных методов. Интерполирование и интегрирование. – Минск: Наука и техника, 1983. 4. Мысовских И.П. Лекции по методам вычислений: учеб. пособие. – СПб.: Изд–во С.Петерб. унта, 1998. 5. Сборник задач по методам вычислений: учеб. пособие / Под ред. П.И. Монастырного, – Минск: Изд. центр БГУ, 2007. 6. Методы вычислений. Интерполирование и интегрирование: курс лекций / М.В. Игнатенко. – Минск: БГУ, 2006.

10. 
Teaching Methods 
Passive, active, interactive, verbal, visual, problematic 
11. 
Teaching language 
Russian 
12. 
Requirements, current control 
– report on laboratory work; – test papers; – colloquium. The score on the exam is set taking into account:40% – current academic performance per semester, 60% – the answer in the exam 
13. 
Method of certification 
Exam 