Mathematical Physics Equations

Description: The main objects of the studied discipline are widely used in applied sciences: thermodynamics, the theory of heat and mass transfer in the mathematical description and modeling of various physical processes. The content of the discipline focuses on mathematical methods that allow you to study various phenomena of the real world by compiling their mathematical models.

Amount of credits: 5

Пререквизиты:

• Ordinary differential equation

Course Workload:

Component: University component

Cycle: Base disciplines

Goal

• Study of mathematical models of the simplest physical processes and basic methods for solving equations of mathematical physics.

Objective

• c- Mastering the basic methods of solving equations of mathematical physics
• - -instilling skills in solving hyperbolic, parabolic and elliptic equations
• - 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.

Assessment of the student's knowledge

Teacher oversees various tasks related to ongoing assessment and determines students' current performance twice during each academic period. Ratings 1 and 2 are formulated based on the outcomes of this ongoing assessment. The student's learning achievements are assessed using a 100-point scale, and the final grades P1 and P2 are calculated as the average of their ongoing performance evaluations. The teacher evaluates the student's work throughout the academic period in alignment with the assignment submission schedule for the discipline. The assessment system may incorporate a mix of written and oral, group and individual formats.

The evaluating policy of learning outcomes by work type

Evaluation form

The student's final grade in the course is calculated on a 100 point grading scale, it includes:

• 40% of the examination result;
• 60% of current control result.

The final grade is calculated by the formula:

 

Where Midterm 1, Midterm 2are digital equivalents of the grades of Midterm 1 and 2;

E is a digital equivalent of the exam grade.

Final alphabetical grade and its equivalent in points:

The letter grading system for students' academic achievements, corresponding to the numerical equivalent on a four-point scale:

Topics of lectures

• Statement of the problem of mathematical physics
• Partial differential equations of the first order
• Classification and reduction to the canonical form of partial differential equations of the second order
• The general solution of the hyperbolic type equation
• General solution of equations of parabolic and elliptic types
• The Cauchy problem for the string oscillation equation
• The Cauchy problem for the equation of thermal conductivity on a straight line
• A mixed problem for the string oscillation equation
• The first boundary value problem for the heat equation
• Integral representation of doubly differentiable functions
• Statement of the main boundary value problems for the Laplace equation
• Solving Laplace's equation in a circle using the Fourier method

Key reading

• А.Н.Тихонов, А.А.Самарский «Уравнения математической физики». Москва 2006 г.
• С.Л.Соболев, «Уравнения математической физики». Москва 2010 г.
• Болсун, А. И. Методы математической физики Минск : Вышэйш. шк., 2008
• Мукашева Р.У. Уравнения математической физики. Конспект лекций. ВКГТУ, 2011
• Чудесенко В.Ф. Сборник заданий по специальным курсам высшей математики. М., «Высшая школа»,2009.
• Будак Б.М. Сборник задач по математической физике./ Б.М. Будак, А.А. Самарский, А. Н. Тихонов, Гостехиздат; 2006
• Будак Б.М. Сборник задач по математической физике./ Б.М. Будак, А.А. Самарский, А. Н. Тихонов, Гостехиздат; 2006

Further reading

• Смирнов М.М. Дифференциальные уравнения в частых производных второго порядка, Наука, 1964.
• Арсенин, В. Я. Методы математической физики и специальные функции. М.: "Наука", 1974.
• Болсун, А. И. Методы математической физики Минск : Вышэйш. шк., 1988