| Lesson Code | Course Name | Class | Credit | Lesson Time | Weekly Lesson Hours (Theoretical) | Weekly Lesson Hours (Practice) | Weekly Class Hours (Laboratory) |
|---|---|---|---|---|---|---|---|
| OTN 6312 | Fundamentals of Operator Theory | Екінші курс | 7 | 210 | 1 | 2 |
The purpose of the discipline is to familiarize students with the methods of the theory of linear operators and their spectral classification related to differential operators. The task of the discipline is to study the main results of spectral theory of a linear operator, methods of analytical research of spectral classification caused by differential operators. As a result of studying the course, undergraduates have: linear operators in Hilbert space. Spectral theory of operators in Hilbert space. Differential operators in a functional space and develops effective mathematical methods for their spectral classification.
Team work, critical thinking, brainstorming, developmental learning method, group project work method, problem method, mini research method, professional skills improvement method, exchange of views, discussion method.
| 1 | Uses a systematic approach and methods of harmonic and intelligent analysis in solving applied problems (LO8); |
| 2 | Develops effective mathematical methods for solving applied problems of mathematics, physics, mechanics, economics and management (LO9). |
| Haftalık Konu | Evaluation Method | |
|---|---|---|
| 1 | Concepts of irrational and inverse problems, examples. | Ауызша және жазбаша |
| 2 | Illogical reports. Proofreading according to adamar. Conditional proofreading. | Ауызша және жазбаша |
| 3 | Proofreading according to Tikhonov.Tikhonov's theorem. | Ауызша және жазбаша |
| 4 | Irrational problems of linear algebra. | Ауызша және жазбаша |
| 5 | Generalization of the concept of a solution. The concept of a normal solution. | Ауызша және жазбаша |
| 6 | The concept of pseudo-solution. | Ауызша және жазбаша |
| 7 | The method of Alpha regularization by A. N. Tikhonov. | Ауызша және жазбаша |
| 8 | The method of M. M. Lavrentiev. | Ауызша және жазбаша |
| 9 | The method of regularization of A. N. Tikhonov. | Ауызша және жазбаша |
| 10 | Gradient methods for solving irrational and inverse problems. | Ауызша және жазбаша |
| 11 | Convergence of gradient methods. | Ауызша және жазбаша |
| 12 | Carlemann Type Estimates. | Ауызша және жазбаша |
| 13 | Carlemann Type Estimates. | Ауызша және жазбаша |
| 14 | The study of the singularity of the solution of Integral-differential equations. | Ауызша және жазбаша |
| 15 | The study of the singularity of the solution of Integral-differential equations. | Ауызша және жазбаша |
| PÇ1 | PÇ2 | PÇ3 | PÇ4 | PÇ5 | PÇ6 | PÇ7 | PÇ8 | PÇ9 |
|---|
| Textbook / Material / Recommended Resources | ||
|---|---|---|
| 1 | A. N. Tıhonov, V.Ia. Arsenın. Qate esepterdi sheshý ádisteri. – M.: Ǵylym, 2014. | |
| 2 | S.I. Kabanıhın. Keri jáne durys emes tapsyrmalar. – Novosıbırsk.: Sibir ǵylymı baspasy, 2014. | |
| 3 | A. A., Samarskıı, P. N. Vabıshevıch. Matematıkalyq fızıkanyń keri esepterin sheshýdiń sandyq ádisteri. – M.: URSS, 2015. | |
| 4 | A. G. Iagola, Van Ianfeı, I. E. Stepanova,, V. N. Tıtarenko. Keri esepter jáne olardy sheshý ádisteri. Geofızıkaǵa qosymshalar. –M.: bınomdyq basylym. Bilim |