Бакалавриат 2025/2026

Численные методы

Статус: Курс обязательный (Прикладная математика)

Кто читает: Департамент прикладной математики

Где читается: Московский институт электроники и математики им. А.Н. Тихонова

Когда читается: 3-й курс, 3, 4 модуль

Охват аудитории: для своего кампуса

Преподаватели: Брандышев Петр Евгеньевич, Рахель Марк Анатольевич

Язык: английский

Кредиты: 3

Контактные часы: 74

Course Syllabus

Abstract

In modern natural sciences the numerical methods play a crucial role. It is related to the fact that modern problems arising in fundamental researches as well as in different applications as a rule have a complicated nature. For example, in such areas as Molecular Biology or Physical Chemistry usually researchers deal with the complex systems containing huge numbers of interacting each other molecules. The problems of such kind results in a serious motivation to develop the reliable numerical methods that are allow solving different problems, which may be reduced to the well-posed mathematical tasks. In this respect, the numerical methods in modern education of mathematicians become indispensable.

Learning Objectives

• Basic command of modern numerical methods of applied maths
• Basic use of common packages and libraries for numeric and scientific computing

Expected Learning Outcomes

• Ability to choose an appropriate numerical method for a given problem

Course Contents

• Root-finding for a single algebraic equation
• Systems of linear algebraic equations
• Function approximation
• Numerical integration
• Numerical differentiation
• Least squares method of function approximation.
• Splines
• Systems of nonlinear algebraic equations
• Function minimization
• Euler method and Runge-Kutta methods
• Ordinary Differential Equations
• Finite element method
• Boundary value problem for ODE
• Partial differential Equations
• Multidimensional constrained minimization

Assessment Elements

• Laboratory work
• In-class assignment
• Activity
• Colloquium
• Colloquium
• In-class assignment
• Activity
• Laboratory work

Interim Assessment

• 2025/2026 4th module
  0.3 * In-class assignment + 0.3 * Laboratory work + 0.1 * Activity + 0.3 * Colloquium
• 2026/2027 2nd module
  0.3 * Colloquium + 0.1 * Activity + 0.3 * In-class assignment + 0.3 * Laboratory work

Bibliography

Recommended Core Bibliography

• Введение в численные методы : учеб. пособие для вузов, Самарский, А. А., 1987
• Вычислительные методы : учеб. пособие, Амосов, А. А., 2014
• Вычислительные методы для инженеров : учеб. пособие для вузов, Амосов, А. А., 2003
• Разностные методы решения краевых задач, Рихтмайер, Р., 1972
• Численные методы, Самарский, А. А., 1989

Authors

• Brandyshev Petr Evgenevich