1.      

Course title

Numerical methods

2.      

Course of Study, Speciality

4,

1-31 03 02 Mechanics and Mathematic Modelling

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

Introduction.

Elements of the theory of errors.

Interpolation and approximation of functions.

Approximate calculation of integrals.

Numerical methods for solving LAA systems.

Calculation of eigenvalues and eigenvectors of matrices.

Solution of nonlinear equations and systems.

Numerical solution of the Cauchy problem for ordinary differential equations.

Numerical solution of boundary value problems for ordinary differential equations.

Numerical solution of Fredholm integral equations.

Construction and investigation of difference schemes for problems of mathematical physics.

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. ун-та, 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