| Lesson Code | Course Name | Class | Credit | Lesson Time | Weekly Lesson Hours (Theoretical) | Weekly Lesson Hours (Practice) | Weekly Class Hours (Laboratory) |
|---|---|---|---|---|---|---|---|
| МТ 1284 | Mathematical analysis І | Бірінші курс | 6 | 180 | 1 | 3 |
Mathematical Analysis I The discipline allows students to understand the limits of a function, the derivative of a function and its geometric, physical meaning. Students learn to solve problems related to a function of one variable. Demonstrates the features of the ability to independently argue abstract thinking and individual statements in solving fundamental mathematical problems of theoretical positions in the scientific and applied direction of mathematics
narrative, exchange of ideas, discussion, problem methods.
| 1 | Uses the rules, laws and methods of mathematics to solve problems in various areas of mathematics (LO 5); |
| 2 | Apply the theoretical knowledge gained in fundamental mathematics to the description of processes and phenomena in various fields of mathematics (LO6); |
| 3 | Использует классические методы математики при решении фундаментальных и прикладных задач. |
| Haftalık Konu | Evaluation Method | |
|---|---|---|
| 1 | Concept of set; Rational numbers; Concept of irrational number; A set of real numbers; | презентация |
| 2 | Absolute value; Limited sets; Interval and segment. | презентация |
| 3 | Variables and constants; Number chains; Uniform chains; e-number; | презентация |
| 4 | Upper and lower limits of the sequence of numbers; The principle of aggregation; Branch chain. | презентация |
| 5 | Limit point concept and Bolzano-Weierstrass theorem; General definition of variable limit; Limit theorems; Infinitely small and infinitely large quantities | Жазбаша |
| 6 | Concept of independent variable and function; Methods of transfer of functions; Geometric representation of the function; Domain of the function; | Жазбаша |
| 7 | Uniform functions; Even, odd and periodic functions; A brief overview of basic elementary functions; Inverse functions; Complex functions; Parametric functions; | презентация |
| 8 | The concept of the limit of the function; Right and left limits of the function; Properties of function limits; | Жазбаша |
| 9 | Continuous functions; Continuity of elementary functions; Continuity of complex functions; | презентация |
| 10 | Intermittent functions; Basic properties of continuous functions. | презентация |
| 11 | A derivative; Concept of differential and its geometric meaning; Derivative and differential of a complex function;The derivative of the inverse function; rules of differentiation of functions; Right and left works; Higher order creations; | презентация |
| 12 | Fermat's and Roll's theorems; Logrange and Cauchy theorems; Clarification of uncertainties; Hospital regulations; Taylor and McLauren formulas; | Жазбаша |
| 13 | Signs of acceleration and deceleration of functions; Maximum and minimum of the function; Study of extremum by second-order derivative | презентация |
| 14 | Sections of tangent and normal; Convex, concavity and bending points; Asymptotes; Ways to create graphs of functions | презентация |
| PÇ1 | PÇ2 | PÇ3 | PÇ4 | PÇ5 | PÇ6 | PÇ7 | PÇ8 | PÇ9 | PÇ10 | PÇ11 |
|---|
| Textbook / Material / Recommended Resources | ||
|---|---|---|
| 1 | Х.И. Ибрашев, Ш.Т. Еркеғұлов. Математикалық анализ курсы. Оқулық. - Новое изд. – Алматы. Экономика, 2014. 562б РМЭБ | |
| 2 | Х.Т. Отаров. Математикалық анализ. Оқулық – Алматы. Экономика, 2012.–536 б. РМЭБ | |
| 3 | О. А. Жәутіков. Математикалық анализ курсы. - Алматы : 'Экономика' баспасы, 2014. - 832 с. РМЭБ | |
| 4 | Кужукеев, Ж.М. Математический анализ: Учебное пособие. - Костанай: КИнЭУ им. М. Дулатова, 2015. - 138c. РМЭБ | |
| 5 | М.Б. Валеева. Математический анализ: Учебно-методический комплекс дисциплины для специальности: 5В010900 - Математика. - Петропавловск: СКГУ им. М. Козыбаева, 2014. - 147c. РМЭБ. |