| Lesson Code | Course Name | Class | Credit | Lesson Time | Weekly Lesson Hours (Theoretical) | Weekly Lesson Hours (Practice) | Weekly Class Hours (Laboratory) |
|---|---|---|---|---|---|---|---|
| FR 32108 | Functional Series | Үшінші курс | 5 | 150 | 1 | 2 |
The discipline introduces to the theory of series. Forms students' skills of quantitative series, their convergence, convergence and uniformity of functional series, classification of functions into power series. Students learn to investigate numerical series for convergence, find the radii of convergence of functional and power series, and consider the classification of Maclaurin and Taylor series by examples.
Group work, blitz-questions, critical thinking, brainstorming, case-stage, developmental teaching method, poster protection creativity teaching methods, Group work, cloud technology, IT method, Case-study method, group project work method, professional skill improvement method, problem composition method, Modular teaching technology.
| 1 | Solves fundamental and applied mathematical problems using basic methods and laws of mathematics (LO 9); |
| 2 | Builds mathematical models of processes and phenomena in solving applied practical problems (LO 10); |
| 3 | Uses theoretical and mathematical-statistical methods in the study of problems in various areas of mathematics (LO 11). |
| Haftalık Konu | Evaluation Method | |
|---|---|---|
| 1 | Number series. Properties of cumulative series. Cauchy criterion of series convergence. | презентация |
| 2 | Comparison of rows. Cauchy, Dalembert, Raabe, Gauss signs of convergence of positive series. | презентация |
| 3 | Strings with variable characters. Absolute and conditional convergence. Leibniz's symbol. | презентация |
| 4 | Dirichlet and Abel signs of convergence. Riemann's theorem. | презентация |
| 5 | Functional chains and series. Smooth compactness. Weierstrass, Dirichlet, Abel signs of uniform compactness. | презентация |
| 6 | Point convergence. Properties of uniformly assembled series and chains. (Continuity, transition to the limit). | презентация |
| 7 | Properties of uniform series and series. (integration, differentiation). | презентация |
| 8 | Endless multiplication, and bringing them into series. | презентация |
| 9 | Degree series. Assembly radius and wheel. Abel's theorem. | презентация |
| 10 | Cauchy-Hadamard formula. Concept of analytical functions. | презентация |
| 11 | Classification of functions into degree series. | презентация |
| 12 | Fourier trigonometric series. Tendency of coefficients of Fourier series to zero. Dirichlet kernel and integral. | презентация |
| 13 | Medium and point compactness. | презентация |
| 14 | Differentiation and integration of Fourier series by terms. | презентация |
| 15 | Smooth convergence and rate of convergence of Fourier series. | презентация |
| PÇ1 | PÇ2 | PÇ3 | PÇ4 | PÇ5 | PÇ6 | PÇ7 | PÇ8 | PÇ9 | PÇ10 | PÇ11 |
|---|
| Textbook / Material / Recommended Resources | ||
|---|---|---|
| 1 | H.I. Ibrashev, Sh.T. Erkeǵulov. Matematıkalyq analız kýrsy. Oqýlyq. - Novoe ızd. – Almaty. Ekonomıka, 2014. 562b RMEB. | |
| 2 | Á.J. Ásibekov, M.D.Qoshanova. Matematıkalyq taldaý: Oqý quraly. 2018j. | |
| 3 | H.T. Otarov. Matematıkalyq analız. Oqýlyq – Almaty. Ekonomıka, 2012.-536 b. RMEB. | |
| 4 | O. A. Jáýtikov. Matematıkalyq analız kýrsy. Oqýlyq.- Almaty : 'Ekonomıka' baspasy, 2014. - 832 s. RMEB. |