Riyazi analiz-2Topics

The basic concepts of numerical series, cumulative series and its sum, properties of cumulative series, residual limit, necessary condition of accumulation and harmonic series are studied.

In the subject, concepts of accumulation and decomposition of numerical series consisting of positive limits are studied. direct and limit comparison signs are examined to determine stacking of rows. the application rules of dalamber and cauchy signs are also explained.

In the subject, the collection of series consisting of positive limits is studied by means of cauchy's integral sign. arbitrary bounded series and their stacking properties are explained. also, the differences between absolute and conditional cumulative series and the rules for their determination are investigated.

Pointwise collection of functional sequences and functional series, as well as the concept of the sum of a functional series are studied in the subject. the concept of regular accumulation and the evaluation of the remainder of the series are explained. also, the application of the weierstrass sign in determining the regular stacking of a functional series is investigated

In the subject, the discontinuity of the sum of functional series and the conditions required for it are studied. the rules of infinite differentiation and integration of functional series are explained. power series, their accumulation region and main properties are also investigated.

In the subject, the continuity of the power series in the area of ​​accumulation, infinite differentiation and integration are studied. the taylor series and the conditions required for the function to separate into this series are explained. also, the separation of some elementary functions into the maclauren series and the binomial series are investigated.

The presentation of periodic functions through the fourier series is studied in the subject. the structure of trigonometric fourier series, calculation of fourier coefficients and basic properties are explained. the separation of the function into the sum of sines and cosines is also investigated.

In the subject, the properties of dividing odd and even functions with 2pi period into fourier series are studied. the calculation of the fourier coefficients for arbitrary periodic functions and the construction of the appropriate series form are explained. also, the writing of fourier series in complex form and determination of complex coefficients are investigated.

In the subject, the concept of multivariable functions and their domain is studied. the limit, discontinuity of a bivariate function and the main properties of these concepts are explained. also, special and complete increments of the function, rules for calculating special derivatives are investigated.

Differentiability of bivariate function, complete differentiation and their existence conditions are studied in the topic. the rules for calculating special derivatives and differentials of higher order are explained. methods of differentiation of complex and non-obvious functions are also investigated.

In the subject, the construction of the equations of the plane tangent to the surface and the normal straight line is studied. directional derivative, gradient and their geometric meaning are explained. methods of determining local, absolute and conditional extrema of a bivariate function are also investigated.

In the topic, the concept of double integral, its definition and main properties are studied. the rules for calculating the repetition of the double integral by means of integrals and substitution of variables are explained. the use of the double integral in solving area, volume and other applied problems is also investigated.

In the subject, data validation tools applied in excel are studied in order to minimize errors caused by the human factor and protect the integrity of the database during the preparation of reports. students analyze constraint mechanisms that ensure that only numbers in a certain range, specific date formats, or predefined drop-down lists can be entered into cells. in the main part of the lesson, the creation of customized warning windows that will appear to the user when entering incorrect information, as well as methods of automatic verification of data accuracy for correct analysis in weekly and month-end reports are practically explored.

In the subject, the concept of type II curvilinear integral and the rules of its parametric calculation are studied. necessary conditions for the integral to be independent of the path of integration are explained. also, the application of green's formula in establishing the relationship between linear and double integrals is investigated.

The chapter summarizes the basic concepts of numerical and functional series, fourier series and multivariable functions for the mathematical analysis-2 course. the calculation, properties, and applications of multiple and line integrals are systematically reviewed. it also examines the relationships between basic theorems, formulas, and methods of solving different types of problems.