Mathematical Physics Equations

Mukasheva Roza Urumkanovna

The instructor profile

Description: Students master methods for solving partial differential equations of various types (elliptic, hyperbolic, and parabolic equations). A large place in the course is occupied by the presentation of the method of separation of variables, the solution of initial-boundary value problems

Amount of credits: 3

Course Workload:

Types of classes hours
Lectures 15
Practical works 15
Laboratory works
SAWTG (Student Autonomous Work under Teacher Guidance) 15
SAW (Student autonomous work) 45
Form of final control Exam
Final assessment method

Component: University component

Cycle: Base disciplines

Goal
  • Providing the necessary knowledge and skills for the formulation, solution and analysis of the results of solving problems of partial differential equations that arise in the modeling of physical objects and processes.
Objective
  • consideration of the main types of equations of mathematical physics and methods of solution,
  • - instilling in the student the skills of constructing mathematical models of practical problems and the skills of choosing an adequate mathematical apparatus for their research;
  • - development of the skill to analyze and practical interpretation of the obtained mathematical results of the study of a real problem;
Learning outcome: knowledge and understanding
  • Know: existing mathematical concepts, methods and models used in the analysis of partial differential equations; analytical methods for solving equations of mathematical physics
Learning outcome: applying knowledge and understanding
  • the ability to solve problems of a mechanical, applied and physical nature using the mathematical apparatus of the course being studied; the development of logical and algorithmic thinking, independent thinking skills, mathematical culture and mathematical intuition, necessary in further work in the study and solution of problems of mechanics, physics, natural science and technology.
Learning outcome: formation of judgments
  • 1.Analyze the behavior of solutions of partial differential equations, based on the results obtained as a result of the study 2. for differential equations, realize selection of classical physics problems and analytical methods for solving them.
Learning outcome: communicative abilities
  • The ability to work in a team in the process of solving practical problems of mechanics, physics, natural science and technology, to express and correctly defend their point of view in controversial issues.
Learning outcome: learning skills or learning abilities
  • strive for professional and personal growth by mastering techniques and skills for solving specific problems from different areas of the discipline, helping to further solve engineering, production and scientific problems
Teaching methods

interactive technologies (with active forms of learning: executive (supervised) conversation; moderation; brainstorming; motivational speech);

independent research work of students during the educational process;

solving educational problems.

Topics of lectures
  • Statement of the problem of mathematical physics
  • Classification and reduction to the canonical form of second-order partial differential equations
  • The Cauchy problem for the equation of string vibrations
  • The Cauchy problem for the wave equation
  • A mixed problem for the equation of string vibrations
  • General scheme of the Fourier method
  • The first boundary value problem for the heat equation
  • Cauchy problems for the heat equation Statement of the problem
  • Integral representation of doubly differentiable functions Green's formula
  • Integral representation
  • Basic boundary value problems for the Laplace equation
  • Solving the internal and external Dirichlet problem for a circle
  • Green's function method Solution of the Dirichlet problem by the Green's function method
  • Finding the Green's function by the method of electrostatic images
  • The definition of the potentials
Key reading
  • 1 Хасеинов, К. А. Каноны математики. Алматы : КазНУ,2003 2 Тихонов А. Н. Уравнения математической физики./ А. Н. Тихонов, А. А. Самарский. Санкт-Петербург : Лань,2012 3. Мукашева Р.У. Уравнения математической физики. Конспект лекций. ВКГТУ, 2011
Further reading
  • 4.Чудесенко В.Ф. Сборник заданий по специальным курсам высшей математики. М., «Высшая школа»,1983. 5 Будак Б.М. Сборник задач по математической физике./ Б.М. Будак, А.А. Самарский, А. Н. Тихонов, Гостехиздат; 1956 6 Кошляков Н.С. Основные дифференциальные уравнения математической физики./ Н.С. Кошляков, Э.Б. Глинер, М.М. Смирнов, Физматгиз, 1962. 7 Смирнов М.М. Дифференциальные уравнения в частых производных второго порядка, Наука, 1964. 8 Арсенин, В. Я. Методы математической физики и специальные функции. М.: "Наука", 1974. 9 Болсун, А. И. Методы математической физики Минск : Вышэйш. шк., 1988