AZTUProgrammes

Subject · Computer science

Kompleks analizTopics

İF- 40164y4 creditsSpring semesterMandatory2025-2026

Topic plan

The subject's topics and the learning outcomes attached to each one.

14 topics

  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

    Topic learning outcomes

    • 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.
    Open resource: Complex numbers and operations on them. (opens in a new tab)

  2. 2. A sequence whose limits are complex numbers

    Lecture

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

    Topic learning outcomes

    • • 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 variable

    Lecture

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

    Topic learning outcomes

    • 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.
    Open resource: A function with a complex variable (opens in a new tab)

  4. 4. Derivative of a function with a complex variable

    Lecture

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

    Topic learning outcomes

    • • must acquire knowledge about complex variable functions, their continuity and differentiation, cauchy-riemann conditions, concept of conformal analysis and regular functions.
    Open resource: Derivative of a function with a complex variable (opens in a new tab)

  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.

    Topic learning outcomes

    • • must acquire knowledge about complex variable functions, their continuity and differentiation, cauchy-riemann conditions, concept of conformal analysis and regular functions.
    Open resource: Concept of differentiability and differentiation of complex variable function. (opens in a new tab)

  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.

    Topic learning outcomes

    • 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.

    Topic learning outcomes

    • Must know integration of complex variable functions, cauchy integral theorem and cauchy integral formula.
    Open resource: Integral of a function with a complex variable. (opens in a new tab)

  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.

    Topic learning outcomes

    • Must know integration of complex variable functions, cauchy integral theorem and cauchy integral formula.
    Open resource: The concept of cauchy-type integral. (opens in a new tab)

  9. 9. Row of laurent

    Lecture

    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.

    Topic learning outcomes

    • Must have knowledge of laurent series and its domain of convergence, classification of isolated eigenpoints of regular functions, complete and meromorphic functions.
    Open resource: Row of laurent (opens in a new tab)

  10. 10. Conditions for separating a function into a laurent series. stacking conditions of the laurent series

    Lecture

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

    Topic learning outcomes

    • Must have knowledge of laurent series and its domain of convergence, classification of isolated eigenpoints of regular functions, complete and meromorphic functions.
    Open resource: Conditions for separating a function into a laurent series. stacking conditions of the laurent series (opens in a new tab)

  11. 11. Disregard of an analytic function to an isolated eigenpoint

    Lecture

    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.

    Open resource: Disregard of an analytic function to an isolated eigenpoint (opens in a new tab)

  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.

    Topic learning outcomes

    • Must know the concept of subtraction, the basic theorem of the theory of subtractions and the calculation of subtractions.
    Open resource: The concept of an infinitely distant point. the concept of logarithmic slope. (opens in a new tab)

  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.

    Topic learning outcomes

    • He should be able to calculate some integrals by subtractions, he should know the principle of argument and rushet's theorem.
    Open resource: Applications of discontinuity theory. the fundamental theorem of algebra. rushe's theorem. applications of the theory of derivatives to the calculation of definite integrals. (opens in a new tab)

  14. 14. General information about analytical continuation. full function concept

    Lecture

    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.

    Topic learning outcomes

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