Riyazi analiz-2Syllabus

Subject code

İF-40163y

Credits

5

Student workload

150

Semester

Autumn semester

Academic year

2025-2026

Subject type

Mandatory

Form of education

Full-time

Language of instruction

Azerbaijani

In-class hours

a) 30 saat-mühazirə b) 30 saat-seminar

Out-of-class hours

a) 54 saat-sərbəst işlər b) 36 saat-hazırlıq

Riyazi analiz–2 fənni çoxdəyişənli funksiyaların diferensial və inteqral hesabının əsas anlayışlarını, çoxqat və əyri xətli inteqralları, səth inteqrallarını, parametrdən asılı inteqralları və funksional sıraları əhatə edir. fənn tələbələrdə riyazi analiz metodlarından istifadə etməklə nəzəri və tətbiqi məsələlərin həlli, analitik təhlil aparılması və kompüter elmlərində rast gəlinən riyazi modellərin qurulması üzrə bilik və bacarıqlar formalaşdırır.

• lecture
• seminar
• interactive discussion
• presentations

1. 1

   CLO 1: Must have knowledge about elements of set theory, concept of limit of sequence, limit and basic properties of univariate function, continuity of univariate function at point and set, regular continuous univariate functions at set.

2. 2

   CLO 2: Derivatives and differentials of a univariate function, basic theorems of differential calculus, high-order derivatives and differentials, taylor's formula for a univariate function, necessary and sufficient conditions for extremum, graphing a function according to characteristic points, indefinite, definite and indefinite integrals and their properties should be known.

3. 3

   CLO 3: Must have knowledge of the concepts and theorems of numerical series, functional sequences and series, power series, taylor and maclauren series and fourier series.

4. 4

   CLO 4: Must know multidimensional euclidean space, limit, discontinuity and regular discontinuity of multivariate function.

5. 5

   CLO 5: Must know special derivatives and differentials of multivariable function, higher order special derivatives and differentials, taylor's formula, necessary and sufficient conditions for extremum.

6. 6

   CLO 6: Must acquire knowledge about parameter-dependent integrals, multiple riemann integrals, differential and surface integrals and be able to calculate them.

1. 1.
   Numerical seriesLecture

   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.

2. 2.
   Sequences with positive limits. comparison signs for sequences with positive terms. dalamber sign. cauchy's sign for the accumulation of a sequence of positive terms.Lecture

   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.

3. 3.
   Cauchy's integral sign. arbitrary signed series with limits. absolute and conditional stacking sequences.Lecture

   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.

4. 4.
   Functional sequence and its assemblyLecture

   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

5. 5.
   Continuity of functional series sum, absolute differentiation and absolute integration. power lines.Lecture

   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.

6. 6.
   Continuity, differentiation and integration of power series. taylor series. conditions for the taylor series decomposition of the function. allocation of some functions to the maclauren range. binomial series.Lecture

   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.

7. 7.
   Fourier series. trigonometric fourier series.Lecture

   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.

8. 8.
   Fourier decomposition of odd and even functions with period 2pi. fourier separation of functions with arbitrary period t=2l. complex form of fourier series.Lecture

   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.

9. 9.
   Concept of multivariable function. limit of bivariate function. continuity of a bivariate function. particular increments, integral increments and particular derivatives of a bivariate function.Lecture

   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.

10. 10.
    Differentiable and differentiable function of two variables. special derivatives of higher order. high build differentials. derivative of a complex function. the derivative of a function given implicitly.Lecture

    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.

11. 11.
    Equations of the plane tangent to the surface and the normal. directional derivative. gradient. the extremum of a bivariate function. the largest and smallest values ​​of the bivariate function in the domain. conditional extremum of a bivariate function.Lecture

    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.

12. 12.
    The concept of double integral. definition and properties of double integral. calculating the double integral. substitution of variables in the double integral. applications of the double integral.Lecture

    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.

13. 13.
    Data validation and data controlLecture

    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.

    • Explains the basic capabilities of the excel environment, data entry, formatting and application of basic functions.
14. 14.
    Curve integral of type II and its calculation. independence of the integration path of type II curve integral. green's formula.Lecture

    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.

15. 15.
    Summary Lecture

    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.

1. Edwin herman, gilbert strang — “calculus, volume 3” — usa–2016(opens in a new tab)