| Lesson Code | Course Name | Class | Credit | Lesson Time | Weekly Lesson Hours (Theoretical) | Weekly Lesson Hours (Practice) | Weekly Class Hours (Laboratory) |
|---|---|---|---|---|---|---|---|
| AI 2296 | Analysis III | Екінші курс | 5 | 150 | 1 | 1 |
The discipline gives the concept of differential calculations of multivariate functions. Develops students ' skills in solving problems on the topic of Integral calculations of multivariate functions and Euler integrals, field theory. Students learn knowledge of curvilinear coordinates, using formulas for calculating multiples of integrals in polar coordinate systems, and practice solving various problems in the scientific and applied direction of mathematics.
Teamwork, problem-based learning, brainstorming. For students with disabilities, together with structural divisions, the teaching methods, forms, type of control and amount of time for the implementation of specialized adaptive disciplines (modules) can be changed by the subject teacher.
| 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 | Euclidean n-dimensional space. Open and closed sets. Circuits in Rn. Compactness in metric space. Multi-variable functions. Limit, independent limits, secondary limits, continuity of multi-variable functions. Independent derivatives and partial differentials. | Жазбаша |
| 2 | Condition for differentiation of multi-argument functions. Insufficient continuity of the discovery of independent derivatives. Differentiation and independent derivatives are non-equivalence of the concept. Differentiation of the composition of functions. Derivative by direction. | Жазбаша |
| 3 | Independent derivatives and differentials of the upper order. Taylor formula. | Жазбаша |
| 4 | Undefined function. Jacobian. The existence and differentiation of functions presented in an undefined form. Extremum of a multivariate function for two variable functions. | Жазбаша |
| 5 | Necessary and sufficient extremum conditions. The extremum of a multivariate function for three variable functions. | Жазбаша |
| 6 | Functional dependence. Conditional extremum. Method of Lagrange multipliers. | Жазбаша |
| 7 | volume in N-dimensional Euclidean space. Riemann multiple integral. finding the Integral of multiple (n=2,3) and its properties. | Жазбаша |
| 8 | Bringing a multiple integral to a secondary integral. Substitution of variables in multiple integrals. | Жазбаша |
| 9 | Сhanging the variables in n-dimensional integrals Curvilinear coordinates. Polar, spherical, cylindrical coordinates. | Жазбаша |
| 10 | Curvilinear integrals of the first and second genera, their properties. Curvilinear integrals independent of the integration path. Green's formula. | Жазбаша |
| 11 | Page. Schwartz for example. Surface area. Surface integrals of the first and second genera. | Жазбаша |
| 12 | Scalar field. Gradient. Vector field. Divergence, rotor. Solenoid, potential vector fields. | Жазбаша |
| 13 | Parameter-dependent eigenvalues. Continuity. | Жазбаша |
| 14 | Parameter-dependent, non-property integrals. Uniform convergence. Weierstrass sign. Properties of a parameter-dependent, non-property integral.Application of parameter-dependent integrals. | Жазбаша |
| 15 | Euler integral of the first genus.(beta and gamma functions.) Euler integral of the second genus. .(beta and gamma functions). | Жазбаша |
| 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. |