| Lesson Code | Course Name | Class | Credit | Lesson Time | Weekly Lesson Hours (Theoretical) | Weekly Lesson Hours (Practice) | Weekly Class Hours (Laboratory) |
|---|---|---|---|---|---|---|---|
| LIOT 3382 | Theory of Measure and Lebegs Integrals | Үшінші курс | 5 | 150 | 1 | 2 |
The discipline introduces students to the basic ideas of the theory of the integral of measurement and Lebesgue for solving applied problems of various natural phenomena. Students apply the basic concepts and methods of the theory of the Lebesgue integral in the study of specific processes. Practicing in solving fundamental and applied mathematical problems using the methods of measurement theory and the Lebesgue integral.
Presentation, exchange of views, discussions, problem methods, situational questions.
| 1 | Uses classical methods of mathematics in solving fundamental and applied problems. (LO 7); |
| 2 | Uses methods of mathematical modeling to solve fundamental and applied practical problems(LO 8); |
| 3 | -Solves the problem, correctly setting the performances of classical problems of fundamental mathematics;(LO 9) |
| Haftalık Konu | Evaluation Method | |
|---|---|---|
| 1 | Set algebras and set algebras. Borel algebra. Measurable functions. | презентация |
| 2 | Dimensions and their continuation. Compact classes. | презентация |
| 3 | The equivalence conditions of the numerical additivity of the measure. The external size and the continuation of the dimensions. | Жазбаша |
| 4 | R^N properties of the Lebesgue measure in space. . Description of dimensional sets | Жазбаша |
| 5 | Dimensional functions in a space with measurable ones. Convergence through dimension. Riesz's theorem. | презентация |
| 6 | Theorems of Egorov and Luzin. -dimensional ratio of functions and A-dimensional functions | Жазбаша |
| 7 | Simple functions. Integral in simple property functions. Lebesgue general definition of the integral. | презентация |
| 8 | Properties of the Lebesgue integral. The absolute continuity of the Lebesgue integral and Chebyshev's inequality. An integrable criterion. The transition to the limit in the Integral. | Жазбаша |
| 9 | The relationship between Lebesgue and Riemann. L^(-1) (μ) space | Жазбаша |
| 10 | Gelders and Minkowski inequalities. L^p (μ) space. Various dimensional functions of the convergence ratio | презентация |
| 11 | The L^∞ (μ) field. The L^p (μ) space and its properties. | презентация |
| 12 | The Radon-Nicodemus theorem. | Жазбаша |
| 13 | Fubini's theorem and adjacent matches. The product of measurements. Notes on infinite dimensions. | презентация |
| 14 | Replacing variables. Scrolls. | презентация |
| 15 | The relationship of the integral and the derivative. Functions whose variation is limited. Absolute continuous functions and the Newton–Leibniz formula. | Жазбаша |
| PÇ1 | PÇ2 | PÇ3 | PÇ4 | PÇ5 | PÇ6 | PÇ7 | PÇ8 | PÇ9 | PÇ10 | PÇ11 |
|---|
| Textbook / Material / Recommended Resources | ||
|---|---|---|
| 1 | Bogachev V. I. Reel analiz üzerine dersler. Lomonosov Moskova Devlet Üniversitesi Yayını. Lomonosov Moskova Devlet Üniversitesi, Moskova, 2008. | |
| 2 | Ulyanov P.L., Bakhvalov A.N. ve diğerleri. Görevlerde Gerçek Analiz. М.: Fizmatlit, 416 s., 2005. | |
| 3 | Dorogovtsev A. Я. Genel ölçü ve integral teorisinin unsurları. Kiev: Vysshaya Okul, Golovnoe Izdvo, 152 s, 1989. |