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Department of Mathematics,
Faculty of Physics, MSU
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Current common courses
Differential equations
Integral Equations and calculus of variations
Introduction to Numerical Methods and Mathematical Modeling in Physics
Linear algebra
Mathematical analysis 2
Numerical methods in physics
Principles of Mathematical Modeling
Special courses
Abstract differential equations with applications in mathematical physics
Asymptotic averaging method for problems of mathematical physics
Asymptotic methods in nonlinear problems of mathematical physics
Asymptotic methods in the theory of differential equations with rapidly oscillating solutions
Catastrophe theory and its applications in physics
Category Theory Basics
Differential inequality method in nonlinear problems
Elliptic equations
Extremal problems
Finite element method in problems of mathematical physics
Functional analysis
Fundamentals of algebra and differential geometry
Gas dynamics and cosmic magnetic fields
Group analysis of differential equations
Introduction to perturbation theory
Linear and nonlinear functional analysis
Mathematical methods in ecology
Mathematical modeling of plasma – kinetic theory
Mathematical modeling of plasma – numerical experiment
Mathematical models of hydrodynamics and gas dynamics
Mathematical problems of diffraction theory
Methods of finite differences in mathematical physics
Modern methods of modeling in magnetohydrodynamics
Nonlinear elliptic and parabolic equations of mathematical physics
Numerical methods in mathematical physics
Parabolic equations
Parallel Computations
Programming of scientific applications in the language C++
Special functions of mathematical physics
Special practical work. Differential schemes
Stochastic differential equations
Supplementary chapters of mathematical physics (nonlinear functional analysis)
Tensor calculus
Theoretical Basics of Big Data Analytics and Real Time Computation Algorithms
Theory of blow-ups of nonlinear equations
Education
Distant education
State exams
Bachelor studies at Faculty of Physics
Bachelor studies at Department of Mathematics
Magistracy
Courses for PhD students
General courses
Special courses
Abstract differential equations with applications in mathematical physics
Asymptotic averaging method for problems of mathematical physics
Asymptotic methods in nonlinear problems of mathematical physics
Asymptotic methods in the theory of differential equations with rapidly oscillating solutions
Catastrophe theory and its applications in physics
Category Theory Basics
Differential inequality method in nonlinear problems
Elliptic equations
Extremal problems
Finite element method in problems of mathematical physics
Functional analysis
Fundamentals of algebra and differential geometry
Gas dynamics and cosmic magnetic fields
Group analysis of differential equations
Introduction to perturbation theory
Linear and nonlinear functional analysis
Mathematical methods in ecology
Mathematical modeling of plasma – kinetic theory
Mathematical modeling of plasma – numerical experiment
Mathematical models of hydrodynamics and gas dynamics
Mathematical problems of diffraction theory
Methods of finite differences in mathematical physics
Modern methods of modeling in magnetohydrodynamics
Numerical methods in mathematical physics
Lukyanenko D. V. videos of lectures
Parabolic equations
Parallel Computations
Programming of scientific applications in the language C++
Special functions of mathematical physics
Special practical work. Differential schemes
Stochastic differential equations
Supplementary chapters of mathematical physics (nonlinear functional analysis)
Tensor calculus
Theoretical Basics of Big Data Analytics and Real Time Computation Algorithms
Theory of blow-ups of nonlinear equations
Special courses for PhD students
Optional courses
Interfaculty courses
Educational olympiads
All courses
Scientific seminars
Devision seminar
Department seminar
Inverse problems in mathematical physics
Mathematical methods in natural sciences
Seminar named after A.B. Vasil'eva: Asimptotic methods in singularly perturbed problems
Lukyanenko D. V. videos of lectures
Лекция 1. Нелинейные уравнения:
Лекция 1. Нелинейные уравнения
Метод дихотомии
Метод простой итерации
Метод Ньютона
Исключение найденных корней
Диагностика кратности корня в методе Ньютона
Обобщённый метод Ньютона
Лекция 2. Решение систем линейных алгебраических уравнений
Метод Гаусса
Пример плохообусловленной системы
Метод Гаусса для системы с трехдиагональной матрицей
Лекция 3. Численное интегрирование
Формулы левых/правых прямоугольников, средних, трапеций
Вывод порядка точности и априорной асимптотически точной оценки погрешности для формулы трапеций
Лекция 4. Вычисления с контролем точности
Формула Рунге-Ромберга
Рекуррентное сгущение сеток и многократное повышение точности по Ричардсону
Повышение точности по Эйткену
Лекция 5. Квазиравномерные сетки
Квазиравномерные сетки, их свойства и сгущение
Вычисление интегралов на квазиравномерных сетках
Вычисление несобственных интегралов
Лекция 6. Интерполяция функций
Задача интерполяции; единственность интерполяционного многочлена
Интерполяционный многочлен Ньютона
Априорная погрешность интерполяционного многочлена Ньютона
Апостериорная погрешность интерполяционного многочлена Ньютона
Параметрическая интерполяция кривых
Решение нелинейных уравнений с помощью интерполяции
Лекция 7. Среднеквадратичная аппроксимация функций
Среднеквадратичная аппроксимация обобщённым многочленом
Неортогональные базисы и обусловленность алгоритма (система степеней)
Ортогональные базисы
Обработка экспериментов. Выбор весов и оптимального числа коэффициентов
Лекция 8. Численное дифференцирование
Постановка задачи
Интерполяционный многочлен Лагранжа
Формула для второй производной (пример)
Несимметричная формула для вычисления первой производной
Вычисления с контролем точности
Примеры
