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Have advanced theoretical and practical knowledge in mathematics and computer science. Week roots of complex numbers, Euler formula 4. Knows programming techniques and is able to write a computer program. Identify, define and model mathematics, computation and computer science problems; select fonksiyon,ar apply appropriate analysis and modeling methods for this purpose.

Establishes one-to-one correspondence between real plane and complex numbers. Define computer programming, word processing, data functions, internete access and software programs. The complex trigonometric functions 7.

Communicate, mathematical ideas both verbally and in written, making use of numerical, graphical, and symbolic viewpoints. Contribution of the Course to Key Yeorisi Outcomes. Algebra of complex numbers.

Finds Taylor and Laurent series of complex functions. Complex power series ,complex Taylor and Mac-Laurin series and Laurent series,classification of the singular points. Classrooms of Arts and Sciences Faculty. Evaluate and interpret data using the knowledge and skills gained in the fields fonksoyonlar mathematics and computer science. Exponential, logarithmic, trigonometric, hyperbolic, inverse lompleks functions.

To be integral in the complex plane, complex power series,Taylor and Laurent series expansions of functions, Singular pointsclassification and komplekx Residue Theorem, some real integrals of complexcalculation methods, the argument of principle. Week hyperbolic function, inverse trigonometric and hyperbolic functions Having the discipline of mathematics, understand the operating logic of the computer and gain the ability to think based on account.

Week addition and multiplication, algebraic properties, vectors and modules, complex congugate 2. Z Course Coordinator Prof. Identify, define and analyze problems in the fields of mathematics and computer science; develop solutions based on research and evidence. Series of complex numbers, complex valuedfunctions 3.

## theory of complex functions

Description of Individual Course Units. Complex numbers, complex plane topology, complex sequences andseries, complex functions, 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 conformal mapping Week analytic functions, harmonic functions, reflection principle Review of the topics discussed in the lecture notes and sources. Describe advanced research methods in the komplfks of Mathematics-Computer Science. Evaluates contour integrals in complex planes. Compulsory Level of Course: Gain an in-depth knowledge on Computer Science including computer programming, word processing, database functions, fonksiyolnar the internet and softwares.

MT Course Type: The complex exponential function, logarithms of complexfunction of the complex power function 6. Liouville’s theorem ,Cauchy’s inequality,essential theorem of algebra,Singularities, zeros and poles. Cauchy-Integral theorem and its consequencesreviews, be analytical functions andseries expansions around some points Week derivatives, differentiations formulas,Cauchy- Riemann equations 8.

Is able to prove Mathematical facts encountered in secondary school. Classifies singular points of complex functions. Complex numbers and their properties, the complexplane topology, complex number sequences fonksiyoonlar.

Expresses clearly the relationship between objects while constructing a model. Have at least one foreign language knowledge and the ability to communicate effectively in Turkish, verbally and in writing.

Possess the teoriei of advanced research methods in mathematics-computer field. Curves classifies the complex planeintegral accounts.

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Theory of Complex Functions Course Code: Demonstrate in-depth feorisi of mathematics, its scope, application, history, problems, methods, and usefulness to mankind both as a science and as an intellectual discipline. Exponential, logarithmic, trigonometric and inverse trigonometric functions, Analytic and harmonic functions. Demonstrate skills in solving problems which require methods of a variety of branches of mathematics to solve them independently or to collaborate with people, and judge reasonable results.

Be aware of the effects of teofisi applications on individual, institutional, social and universal dimensions and have the awareness about entrepreneurship, innovation. Week Final Exam 2nd. Limits and continuity, differentiation 4.