| Lesson Code | Course Name | Class | Credit | Lesson Time | Weekly Lesson Hours (Theoretical) | Weekly Lesson Hours (Practice) | Weekly Class Hours (Laboratory) |
|---|---|---|---|---|---|---|---|
| KAFT 4387 | Theory of Functions of a Complex Variable | Үшінші курс | 5 | 150 | 1 | 2 |
In teaching the course, it is important to get acquainted with the fundamental ways of studying complex variables. These approaches are based on the analysis of infinitesimal values and the use of the properties of the field of complex numbers. In this subject, students learn methods of studying complex variable functions. Students understand the theoretical and practical foundations of understanding the various methods of using complex variable functions for the study of mathematical objects, and practice the methods of making decisions based on mathematical modeling in the study of ideas and problems.
Narrative, exchange of ideas, discussion, problem methods, situational questions.
| 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 | Conducts scientific and pedagogical research in the educational environment (LО11). |
| Haftalık Konu | Evaluation Method | |
|---|---|---|
| 1 | Complex numbers and applying operations to them. Set of complex numbers and its geom. Interpretation. Algebraic form of a complex number. Operations on complex numbers. The modulus of a complex number. Argument of a complex number. Compl. number trigonometer. type. | презентация |
| 2 | Moivre's formula Finding the root of a complex number Type of computer number indicator Logarithm comp. | презентация |
| 3 | Complex variable function. Limit and continuity of complex variable function. | презентация |
| 4 | Differentiation of complex variable functions Cauchy-Riemann conditions. Analytical function. Differential. The geometric meaning of the product. Concept of conformal representation. | презентация |
| 5 | Concept of analytic function. Simple properties of analytic functions. Relationship between analytic and harmonic functions. | презентация |
| 6 | Linear and linear-partial functions Power function. Concept of Riemann surface. | презентация |
| 7 | The corset is not a logarithmic function. Zhalpy turdegi dәrezhelіk function. Trigon. Functionlar. | презентация |
| 8 | Integration of a complex variable function. Definition, properties and calculation rules of integration. | презентация |
| 9 | Integral of analytical functions. Cauchy's theorem for a connected domain. Independence of the integral from the path of integration. | презентация |
| 10 | Higher order derivatives of analytic function. | презентация |
| 11 | Degree series in the complex region. Taylor series. Classification of functions into degree series. | презентация |
| 12 | Laurent series. | презентация |
| 13 | Zeros of the analytic function. Special points. Pole. Special secluded spots. Fixed points. | презентация |
| 14 | Residue of a function at a singular point Calculation of the residual. | презентация |
| 15 | Calculating integrals using the derivative. Calculation of improper integrals. | презентация |
| PÇ1 | PÇ2 | PÇ3 | PÇ4 | PÇ5 | PÇ6 | PÇ7 | PÇ8 | PÇ9 | PÇ10 | PÇ11 |
|---|
| Textbook / Material / Recommended Resources | ||
|---|---|---|
| 1 | E. J Aydos Kompleks aynımaldı fwnkcïyalar teorïyası jäne operacïyalıq eseptewler. Oqw quralı. - Almatı: 2015j. | |
| 2 | E. J Aydos Kompleks aynımaldı fwnkcïyalar teorïyası jäne operacïyalıq eseptewler. Oqw quralı. - Almatı: 2015j. | |
| 3 | Otarov X.T. Matematïkalıq analïz. Oqw quralı. Almatı 2012. |