1. 
Title of discipline 
Generalized functions 
2. 
Course of study, specialty 
1, 131 80 03 Mathematics 
3. 
Semester of training (for each semester a separate table) 
2 
4. 
Number of credits (curriculum) 
3 
5. 
Name and surname lecturer 
Antonevich Anatoly Borisovich 
6. 
Objectives of the study of the discipline 
Familiarization of students with the main ways of mathematical formalization of conflict situations in the economic and social spheres and the principles of their solution. Training in various effective ways to resolve conflict situations, taking into account the interests of the conflicting parties. Increase the overall level of mathematical culture and improve the skills of using mathematical methods to solve applied problems. As a result of studying the discipline, the trainee must know:
be able to:
own:

7. 
Prerequisites 
Fundamentals of mathematical analysis Fundamentals of functional analysis Differential equations 
8. 
Contents of the discipline 
Theme 1. The space of basic functions. Convergence, operations of differentiation and multiplication by a smooth function. Topology of the space of basic functions. Theme 2. The space of generalized functions. Definition of a generalized function. Convergence in the space of generalized functions. Differentiation of generalized functions. Differentiation of discontinuous functions. Multiplication by smooth functions. The basic generalized functions xα. Theme 3. Convolution of generalized functions. Fundamental solutions for differential equations with constant coefficients. Theme 4. Topological vector spaces. Locally convex topological vector spaces. Topology in spaces of basic and generalized functions. Theme 5. The Fourier transform of generalized functions. The Schwartz space of moderately growing distributions. The Fourier transform. Construction of fundamental solutions using the Fourier transform. Theme 6. Periodic generalized functions. Spaces of basic periodic functions. Periodic generalized functions. Fourier series. 
9. 
Recommended Reading 
Basic

10. 
Methods of teaching 
Lectures, UIRS 
11. 
Language of learning 
Russian 
12. 
Conditions (requirements), routine control 
Test papers

13. 
Appraisal form 
credit
