| Lesson Code | Course Name | Class | Credit | Lesson Time | Weekly Lesson Hours (Theoretical) | Weekly Lesson Hours (Practice) | Weekly Class Hours (Laboratory) |
|---|---|---|---|---|---|---|---|
| AI 2294 | Analysis II | Екінші курс | 4 | 120 | 1 | 1 |
The discipline deepens acquaintance with the theory of mathematical analysis. Teaches solving problems on the topic of integral calculations of functions of one variable and its application. Introduces students to the primitive function, the concept of an indefinite integral and the properties of an indefinite integral. Students learn to find the primitive function of a function using the methods of integration by parts and replacement of variables, integration of rational fractions and the Ostrogradsky method.
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 | The concept of the first function. The concept of indefinite integral. Properties of the indefinite integral. Table of fundamentals of indefinite integrals. Integration by parts and change of variable. | |
| 2 | Integration of rational fractions Ostrogradsky method. | |
| 3 | Integrating irrational, differential binomials. | |
| 4 | Integration of trigonometric and transcendental functions. | |
| 5 | Problems that give rise to the concept of a definite integral. The limit of the integral sum. Upper and lower integral Darboux sums and their properties. | |
| 6 | Necessary and sufficient conditions for integration. Classes of integrable functions. | |
| 7 | Properties of the definite integral. Mean value theorems. | |
| 8 | A definite integral, the upper limit of which is variable. The Newton-Leibniz formula. | |
| 9 | Integral calculation methods are defined. (variable substitution, division). | |
| 10 | Approximation of defined integrals. Calculation of the area of flat figures in the Cartesian coordinate system. Calculation of the area of flat figures in the polar coordinate system. | |
| 11 | Arc length and differential. Calculation of volumes. | |
| 12 | Surface area of rotation Center of gravity. Moment of inertia. | |
| 13 | Propertyless integrals whose limits are infinite. | |
| 14 | Absolute set propertyless integrals. | |
| 15 | Integrals of undefined functions. |
| 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 | O. A. Jáýtikov. Matematıkalyq analız kýrsy. Oqýlyq.- Almaty : 'Ekonomıka' baspasy, 2014. - 832 s. RMEB. | |
| 4 | B.T. Qalymbetov Kóp aınymaly fýnksıalar. 'Matematıkalyq taldaý' kýrsy boıynsha oqý- ádistemelik qural. Túrkistan, 2015. | |
| 5 | V.A.Mamaeva. Matematıkalyq taldaýdan tájirıbelik jumystardy oryndaýǵa arnalǵan ádistemelik nusqaý. 2-bólim. Oqý-ádistemelik qural. 2017j. |