| Lesson Code | Course Name | Class | Credit | Lesson Time | Weekly Lesson Hours (Theoretical) | Weekly Lesson Hours (Practice) | Weekly Class Hours (Laboratory) |
|---|---|---|---|---|---|---|---|
| МKMA 6309 | Mathematical Analysis on Metric Spaces | Екінші курс | 7 | 210 | 3 | 4 |
The purpose of the discipline is to develop skills in solving non-standard, non-typical applied problems of modern mathematical analysis in metric spaces and stochastic analysis, as well as to form readiness for independent professional activity with some of their applications. Studies new mathematical methods of basic concepts and important fundamental results of the general theory of random processes. Develops constructive methods for the theory of Martingale and semi-partingal.
Teamwork, critical thinking, brainstorming, the method of developmental learning, the method of group project work, the problem method, the method of mini-research, the method of increasing professionalism, the method of exchanging opinions, discussions.
| 1 | Pon 1-develops constructive methods for solving boundary value problems for integral differential equations; |
| 2 | PON 2-studies new mathematical methods for solving extreme problems and limit problems for nonlinear differential equations and mathematical physics. |
| Haftalık Konu | Evaluation Method | |
|---|---|---|
| 1 | Metric spaces. Examples. | Жазбаша |
| 2 | Continuous images of metric spaces. Completeness. Convergence in the language of 'neighborhood'. | Жазбаша |
| 3 | Heine convergence. Closed and open meetings. Complete metric spaces. | Жазбаша |
| 4 | The nested balls theorem. Dense insides. Baer's theorem. | Жазбаша |
| 5 | Completeness and solvability of equations. Filling the space. | Жазбаша |
| 6 | The principle of image compression. Application in solving ordinary differential equations and integral equations. | Жазбаша |
| 7 | Linear, normalized, and Euclidean spaces. | Жазбаша |
| 8 | Orthogonal systems. The orthogonalization theorem. Fourier coefficients. Bessel's inequality. | Жазбаша |
| 9 | Functions. Compact sets in metric spaces. The Arcela theorem. | Жазбаша |
| 10 | Properties of continuous linear functionals. The Khan-Banach theorem. The nodal space. | Жазбаша |
| 11 | Generalized functions. The derivative of the generalized function. Differential equations of a class of generalized functions. | Жазбаша |
| 12 | The linear operator. The operator's norm. A wide range of linear operators. Compact operators. | Жазбаша |
| 13 | The principle of uniform manipulation. The Banach-Steingauz theorem. Dead-end operators. The closed graph theorem. | Жазбаша |
| 14 | The nodal operator. The operator equation. The inverse operator. | Жазбаша |
| 15 | Intermittent tension. A sufficient condition. The spectrum of the operator. The resolvent. Compact operator spectrum. | Жазбаша |
| PÇ1 | PÇ2 | PÇ3 | PÇ4 | PÇ5 | PÇ6 | PÇ7 | PÇ8 | PÇ9 |
|---|
| Textbook / Material / Recommended Resources | ||
|---|---|---|
| 1 | Kolmogorov A.N. Elementy teorii funksi i funksionälnogo analiza. – M.: Fizmatlit, 2014. | |
| 2 | Trenogin V.A. Funksionälnyi analiz/ V.A. Trenogin. – M.: Nauka, 2017. | |
| 3 | Şilov G.E. Matematicheski analiz. Vtoroi spesiälnyi kurs/ G.E. Şilov. – M.: MGU, 2013. | |
| 4 | Baharev F.L. Osnovy funksionälnogo analiza. Uchebnoe posobie. – SPb.: İzd-i dom S.-Peterb.gos. un-ta., 2012. |