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Describe advanced research methods in the field of Mathematics-Computer Science.

kompleks fonksiyonlar teorisi

Possess theoretical and practical knowledge in mathematics, computation and computer science. Follow current developments about the awareness of the necessity of continuous professional development and information and communication technologies.

Use the time effectively in the process of getting the conclusion with analytical thinking ability. Algebra of complex numbers. Classifies singular points of complex functions. Cauchy-Integral theorem and its consequencesreviews, be analytical functions andseries expansions around some points.

Cauchy-Riemann equations and analyticity 5. Curves classifies the complex planeintegral accounts. Complex exponential ,complex power ,complex logarithmic and complex trigonometric functions. To be integral in the complex plane, complex power series,Taylor and Laurent series expansions of functions, Singular pointsclassification and the Residue Theorem, some real integrals of complexcalculation methods, the argument of principle.


Have the consciousness of the necessity of lifelong learning and continuously develop professional knowledge and skills.

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This course komplekz to investigate complex numbers, their notations and properties and introduction of the complex functions theory and give the complex sequences and series ,the conceptions of limit,continuity,complex differentation and kompleos functions and theorems related with these and applications. Evaluate and interpret data using the knowledge and skills gained in the fields of mathematics and computer science.

Complex numbers, complex plane topology, complex sequences andseries, complex foknsiyonlar, limits, continuity and derivatives, Cauchy-Riemannequations, Analytic, complex exponential, logarithmic, trigonometric, andhyperbolic functions, integration in the complex plane, Cauchy’s theorem,Complex power series, Taylor and Laurent series expansions, Singularclassification of points and the Residue Theorem, some real integralscomplex calculation methods, the argument of principle.

Week hyperbolic function, inverse trigonometric and hyperbolic functions Sufficient conditions for derivatives, analytic functions, harmonic functions. Contribution of the Course to Key Learning Outcomes.

Evaluates contour integrals in complex planes. Preliminary Weekly and Related Topics Pages 1. Complex power series ,complex Taylor komppeks Mac-Laurin series and Laurent series,classification of the singular points. Week stereografic mapping, regions in the complex plane 5. Week limits, theorems on limits, limits involving infinity, continuity 7. Perform all phases of life cycle in computer based systems.

Draws mathematical models such as formulas, graphs and tables and explains them. Assessment Methods and Assessment Criteria.


theory of complex functions

MT Course Type: Identify, define and model mathematics, computation and computer science problems; select and apply appropriate analysis and modeling methods for this purpose. Exponential, logarithmic, trigonometric, hyperbolic, inverse trigonometric functions. Week Theoretical Practice Laboratory 1. Utilize technology as an effective tool in investigating, understanding, and applying mathematics.

Have the awareness of professional and ethical responsibility and legal consequences of information applications Use the knowledge about the field for the benefit to society. Finds images of certain sets under complex linear functions and some elementary functions.

Be aware of the effects of information applications on individual, institutional, social and universal dimensions and have the awareness about entrepreneurship, innovation. Basic fonsiyonlar of comlex numbers, Polar forms, powers, roots, domains. Is able to mathematically reorganize, analyze and model problems encountered.

Design and apply interactive experimental environments to get the definitions and first solutions of the problems of computer science and computer science and fonksitonlar these environments.