Mathematical analysis

Description

The subject involves the formation of students' fundamental theoretical knowledge of mathematical analysis and the ability to use this knowledge in solving various problems. within the scope of the subject, the concepts of sets and real numbers, numerical sequences, univariate and multivariate functions, limit, continuity and regular continuity are studied. differential calculus of univariate functions, primitive function, indefinite and definite integrals, as well as applications of integral calculus are reviewed. numerical and functional series and basic properties of multivariable functions are also explored. the subject is aimed at developing students' ability to build algorithms for solving mathematical problems, evaluate their effectiveness, and use mathematical analysis methods in solving problems of applied mathematics, informatics, and cryptology.

Course learning outcomes

1. 1

   CLO 1: He should know the definition of the limit of a sequence, the concepts of stacking and collapsing sequences, some properties of the limit.

2. 2

   CLO 2: Must have knowledge about the limit of a function, the definition of a function that is continuous at a point, its basic properties, and points of discontinuity.

3. 3

   CLO 3: Must have knowledge about the definition of the derivative of a function, its basic properties, the definition of the differential at a point and related theorems. the definition of the maximum and minimum points of the function, the necessary condition for the extremum, the first and the second sufficient conditions should be acquired.

4. 4

   CLO 4: It should have information about the division of the part, its properties, the definition of the definite integral, the classes of integrated functions.

5. 5

   CLO 5: He should know the definition of a numerical sequence, the necessary condition and the properties of the cumulative sequence. collection radius and collection interval of power series. the cauchy-adamar formula must be mastered with information about the taylor series.

6. 6

   CLO 6: Must acquire knowledge about special derivatives and differential of multivariable function.