Kompleks analizSyllabus

Subject code

İF- 40164y

Credits

4

Student workload

120

Semester

Spring 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) 15 saat - seminar

Out-of-class hours

a) 45 saat - sərbəst işlər b) 30 saat - hazırlıq

Kompleks analiz fənni kompleks ədədlər, kompleks dəyişənli funksiyalar, analitik funksiyalar, koşi-riman şərtləri, kompleks inteqrallar, koşi inteqral teoremi və düsturu, loran sıraları, çıxıqlar nəzəriyyəsi və kompleks inteqral hesabının əsaslarını əhatə edir. fənn tələbələrdə kompleks dəyişənli funksiyaların xassələrini təhlil etmək, kompleks inteqralları hesablamaq, analitik üsullardan istifadə etməklə riyazi və mühəndislik məsələlərini modelləşdirmək və həll etmək bacarıqlarının formalaşdırılmasına xidmət edir.

• lecture
• seminar
• presentations
• interactive discussion

1. 1

   CLO 1: The concept of complex number, operations on complex numbers, argument and modulus of a complex number, trigonometric form of a complex number, euler's formula, power of a complex number, subtraction from a complex number and expanded complex plane should have knowledge.

2. 2

   CLO 2: Complex variable functions, their continuity and differentiation, cauchy-riemann conditions, the concept of conformal analysis should acquire knowledge about verregular functions.

3. 3

   CLO 3: He should know integration of complex variable functions, cauchy integral theorem, cauchy integral formula.

4. 4

   CLO 4: Must have knowledge about laurent series and its collection domain, classification of isolated eigenpoints of regular functions, complete and meromorphic functions.

5. 5

   CLO 5: He should know the concept of deficit, the main theorem of the theory of deficits and the calculation of deficits.

6. 6

   CLO 6: He should be able to calculate some integrals through subtractions, he should know the principle of argument and rushet's theorem.

1. 1.
   Complex numbers and operations on them.Lecture

   Expression of complex numbers in different forms, actions on them, application of muavr and euler's formulas are studied in the subject

   • The concept of complex number, operations on complex numbers, argument and modulus of a complex number, trigonometric form of a complex number, euler's formula, power of a complex number, expansion from a complex number and expanded complex plane should have knowledge.
2. 2.
   A sequence whose limits are complex numbersLecture

   Sequences of complex numbers, their limit and accumulation conditions are studied in the subject.

   • • must acquire knowledge about complex variable functions, their continuity and differentiation, cauchy-riemann conditions, concept of conformal analysis and regular functions.
3. 3.
   A function with a complex variableLecture

   Complex variable functions, their main types, limit and continuity conditions are studied in the subject.

   • It is necessary to acquire knowledge about complex variable functions, their continuity and differentiation, cauchy-riemann conditions, the concept of conformal analysis and regular functions.
4. 4.
   Derivative of a function with a complex variableLecture

   Derivation of complex variable function, monogenic and analytic functions, as well as cauchy-riemann conditions are studied in the subject.

   • • must acquire knowledge about complex variable functions, their continuity and differentiation, cauchy-riemann conditions, concept of conformal analysis and regular functions.
5. 5.
   Concept of differentiability and differentiation of complex variable function.Lecture

   Differentiability of a function with a complex variable, the concept of differentiation and the rules of differentiation of elementary functions are studied in the subject.

   • • must acquire knowledge about complex variable functions, their continuity and differentiation, cauchy-riemann conditions, concept of conformal analysis and regular functions.
6. 6.
   A numerical sequence of complex numbers.

   In the subject, summability and summation of complex numerical series, power series, abel's i theorem, radius of accumulation and circle of accumulation are studied.

   • Must have knowledge of laurent series and its domain of convergence, classification of isolated eigenpoints of regular functions, complete and meromorphic functions.
7. 7.
   Integral of a function with a complex variable.Lecture

   In the subject, the integral of a complex variable function, its main properties, cauchy's theorem and cauchy's integral formula are studied.

   • Must know integration of complex variable functions, cauchy integral theorem and cauchy integral formula.
8. 8.
   The concept of cauchy-type integral.Lecture

   In the subject, cauchy-type integral, separation of analytic functions into power series, weierstrass theorems, cauchy's inequality and liouville's theorem are studied.

   • Must know integration of complex variable functions, cauchy integral theorem and cauchy integral formula.
9. 9.
   Row of laurentLecture

   In the subject, the division of analytic functions into laurent series, the uniqueness of the division, and the right and prime parts of the series are studied.

   • Must have knowledge of laurent series and its domain of convergence, classification of isolated eigenpoints of regular functions, complete and meromorphic functions.
10. 10.
    Conditions for separating a function into a laurent series. stacking conditions of the laurent seriesLecture

    In the topic, the conditions of separation of the function into the loran series and the domain of accumulation of this series are studied.

    • Must have knowledge of laurent series and its domain of convergence, classification of isolated eigenpoints of regular functions, complete and meromorphic functions.
11. 11.
    Disregard of an analytic function to an isolated eigenpointLecture

    In the subject, the deviation of an analytic function to an isolated specific point, the main theorem about deviations, and the methods of calculating the deviation at the pole point are studied.

12. 12.
    The concept of an infinitely distant point. the concept of logarithmic slope.Lecture

    In the subject, the rules for calculating the logarithmic deviation of a function at an infinitely distant point are studied.

    • Must know the concept of subtraction, the basic theorem of the theory of subtractions and the calculation of subtractions.
13. 13.
    Applications of discontinuity theory. the fundamental theorem of algebra. rushe's theorem. applications of the theory of derivatives to the calculation of definite integrals.Lecture

    In the subject, applications of the theory of offsets to the main theorem of algebra, rouchet's theorem and the calculation of definite integrals are studied.

    • He should be able to calculate some integrals by subtractions, he should know the principle of argument and rushet's theorem.
14. 14.
    General information about analytical continuation. full function conceptLecture

    In the subject, the concept of analytic continuation, the extension of the domain of the function, and the main characteristics of complete functions are studied.

    • Must know the concept of subtraction, the basic theorem of the theory of subtractions and the calculation of subtractions.

1. R.y. shukurov, t.b. asadov, "theory of functions with complex variables", azerbaijan-2012(opens in a new tab)
2. Russell howell, john mathews, "complex analysis: an open source textbook", usa-2025(opens in a new tab)