| Lesson Code | Course Name | Class | Credit | Lesson Time | Weekly Lesson Hours (Theoretical) | Weekly Lesson Hours (Practice) | Weekly Class Hours (Laboratory) |
|---|---|---|---|---|---|---|---|
| DZhOT 5215 | Theory of Stability of Dynamic Systems | Бірінші курс | 5 | 150 | 1 | 2 |
The purpose of the discipline is to master the basic concepts of dynamical systems theory, stability theory; to form concepts such as chaos, Strange Attractor, fractal; to form concepts of quantitative integration of dynamical systems, areas of application of dynamical systems in technology and biology. Methods of stability research. Analyzes current trends in the study of stability in the digital regulator system. Develops effective mathematical methods for solving problems of stability theory.
narrative, exchange of ideas, discussion, problem methods.
| 1 | Analyzes current development trends, the main problems of the history and philosophy of science, possession of the conceptual and methodological apparatus and applying the theoretical knowledge gained in various forms of research and intercultural communication |
| 2 | Studies new mathematical methods for solving extreme problems and boundary value problems for nonlinear differential equations and mathematical physics |
| 3 | Uses a systematic approach and methods of harmonic and intelligent analysis in solving applied problems |
| Haftalık Konu | Evaluation Method | |
|---|---|---|
| 1 | Matrix functions. Matrix rows. | презентация |
| 2 | The exponential of a matrix. The logarithm of a matrix. | Жазбаша |
| 3 | Basic theory of stability understanding. | Жазбаша |
| 4 | Ostrogradsky - Liouville formula. | презентация |
| 5 | Hurwitz criterion | Жазбашапрезентация |
| 6 | Mikhailov criterion. | презентация |
| 7 | Gronwalla Belman and Bihari lemmas. | презентация |
| 8 | Characteristics of functions indicator. | презентация |
| 9 | System of homogeneous equations spectrum. | Жазбаша |
| 10 | Deliverable systems. Erugin theorem. | презентация |
| 11 | Cited systems. | презентация |
| 12 | Character defined functions. | Жазбаша |
| 13 | Lyapunov's first theorem. | презентация |
| 14 | Lyapunov's second theorem. | Жазбашапрезентация |
| 15 | Lyapunov's third theorem. | презентация |
| PÇ1 | PÇ2 | PÇ3 | PÇ4 | PÇ5 | PÇ6 | PÇ7 | PÇ8 | PÇ9 |
|---|
| Textbook / Material / Recommended Resources | ||
|---|---|---|
| 1 | Demıdovıch B.P. Leksıı po matematıcheskoı teorıı ýstoıchıvosı. M. 'Naýka': 1967; | |
| 2 | Demıdovıch B.P., Maron I.A. Osnovy vychıslıtelnoı matematıkı M. 'Naýka': 1966; | |
| 3 | Malkın I.G. Teorıa ýstoıchıvostı dvıjenıa. M. 'Naýka': 1966; | |
| 4 | Chetaev N.G. Ýstoıchıvos dvıjenıa. 'Gostehızdat': 1955; | |
| 5 | Stepanov V.V Kýrs dıfferensıalnyh ýravnenıı M.Fızmatgız 1959 |