Principles of Mathematical Modeling

The course contains a systematic presentation of the basic concepts and principles of mathematical modeling, examples of mathematical models of physical processes and phenomena, and modern methods of investigation of these models.

Read at 6-st semester.
2 hours of lectures per week, practical work

• Bogolubov Aleksandr Nikolaevich
• Tikhonov Nikolai Andreevich
• Tokmachev Michael Gennadevich

• Basic concepts and principles of mathematical modeling.
• Some classical problems of mathematical physics.
• Mathematical modeling of nonlinear objects and processes.
• Basic research methods mathematical tools.
• Some of the new objects and methods of mathematical modeling.

The course "Principles of mathematical modeling" contains a systematic presentation of the basic concepts and principles of mathematical modeling, examples of mathematical models of physical processes and phenomena, and modern methods of investigation of these models. The course should serve as a basis for the formation of mathematical modeling skills in specific areas of physics. The course follows immediately after the course "Methods of Mathematical Physics", being its continuation and development of, and precedes the course "Numerical Methods".
The workshop is an integral part of the course consists of two tasks:

1. Numerical solution of the transport equation.
2. The numerical solution of the initial-boundary value problem for the two-dimensional heat equation without using standard libraries for solving differential equations.

Under each objective of the workshop students will receive a brief description containing all the information necessary for its implementation, and make out a report.

• A.N. Bogolyubov, N.A. Tikhonov, Mitin I.V., Shapkina N.E. Examples of tasks for the course "Fundamentals of Mathematical Modeling"
• The method of solution of the first practical assignment
• The method of solution of the second practical assignment

1 stream:

• The plan of lectures
• The course program
• Questions for the written part of the exam on the course

2 stream:

• Questions to the Colloquium on the course "Fundamentals of Mathematical Modeling"
• The course program
• Questions for the written part of the exam on the course

Summary of A.N. Bogolyubov's lectures 

• Lecture - 1
• Lecture - 2
• Lecture - 3
• Lecture - 4
• Lecture - 5
• Lecture - 6
• Lecture - 7
• Lecture - 8
• Lecture - 9
• Lecture - 10
• Lecture - 11
• Lecture - 12
• Lecture - 13

Additional materials for A.N. Bogolyubov lectures 

• The Goursa problem
• Riemann function
• Stefan problem
• The problem of sorption
• The Helmholtz equation
• Nonlinear heat conduction
• Nonlinear waves
• Singular perturbations