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: 4-й курс, 1 модуль

Охват аудитории: для своего кампуса

Преподаватели: Брандышев Петр Евгеньевич, Рахель Марк Анатольевич

Язык: английский

Кредиты: 3

Контактные часы: 28

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 equations: direct methods.
• 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

Assessment Elements

• Laboratory works
• Control work
• Exam-1
• Exam-2
• Laboratory work
• Attendance
• Attendance
• Control work

Interim Assessment

• 2024/2025 4th module
  0.4 * Laboratory works + 0.2 * Control work + 0.3 * Exam-1 + 0.1 * Attendance
• 2025/2026 1st module
  0.1 * Attendance + 0.2 * Control work + 0.3 * Exam-2 + 0.4 * 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
• Теория разностных схем : учеб. пособие, Самарский, А. А., 1989
• Численные методы, Самарский, А. А., 1989

Recommended Additional Bibliography

• Теория разностных схем, Самарский, А. А., 1977

Authors

• Brandyshev Petr Evgenevich