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Complex numbers and their properties, the complexplane topology, complex number sequences 2. Week complex valed functions, mappings, mapping by the exponential function 6.

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. Have at least one foreign language knowledge and the ability to communicate effectively in Turkish, verbally and in writing.

Associate’s Degree Short Cycle. Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians. Giving a series of numbers and series of complex. Define computer programming, word processing, data functions, internete access and software programs.

None Recommended Optional Programme Components: Week hyperbolic function, inverse trigonometric and hyperbolic functions Basic properties of comlex numbers, Polar forms, powers, roots, domains. Utilize technology as an effective tool in investigating, understanding, and applying mathematics.

### Encode Explorer

Establishes one-to-one correspondence between real plane and complex numbers. Recognizes the importance of basic notions in Algebra, Analysis and Topology. Uses effective scientific methods and appropriate technologies to solve problems. This course aims 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 entire functions and theorems related with these and applications.

Week stereografic mapping, regions in the complex plane 5. Week roots of complex numbers, Euler formula 4.

### Ders Tanım ve Uygulama Bilgileri

Week analytic functions, harmonic functions, reflection principle Knows programming techniques and is able to write a computer program. Having the discipline of mathematics, understand the operating logic of the computer and gain the ability to think based on account.

General Information for Students. Express habits of effective komplekks involving analytical, critical and postulational thinking as well as reasoning by analogy and the development of intellectual thinking. Week Final Exam 1st. Follow current developments about the awareness of the necessity of continuous professional development and information and communication technologies.

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.

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

## Description of Individual Course Units

Sufficient conditions for derivatives, analytic functions, harmonic functions. Identify, define and analyze problems in the fields of mathematics and computer science; develop solutions based on research and evidence. First Cycle Year of Study: Cultivate the perspectives and the analytical skills required for efficient use, appreciation, and understanding of mathematics. Week Final Exam 2nd. Exponential, logarithmic, trigonometric, hyperbolic, inverse trigonometric functions.

Finds Taylor and Laurent series of complex functions. Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. Week derivatives, differentiations formulas,Cauchy- Riemann equations 8. Algebra of complex numbers. Compulsory Level of Course: This course covers complex numbers and its basic properties ,topology of the complex plane ,sequence and series of complex numbers, complex valued functions and its basic propertieslimit and continuity of the complex valued functions, complex differentationof the complex valued functions ,Cauchy-Riemann’s equationscomplex exponential ,complex power ,complex logarithmic and complex trigonometric functionsanalytic and harmonic functionsintegration of complex valued functionsCauchy’s integral theorem and Cauchy’s integral ,the derivative of Cauchy formula and applicationsLiouville’s theorem ,Cauchy’s inequality,esential theorem of algebra,Singularities, zeros and poles ,complex power series ,complex Taylor and Mac-Laurin series and Laurent series,classification of the singular points, residues,residue theorem and applicationsconform tranformations.

Is able to express basic theories of mathematics properly and correctly both written and verbally. Identify, define and model mathematics, computation and computer science problems; select and apply appropriate analysis and modeling methods for this purpose.

Z Course Coordinator Prof. Complex numbers, complex plane topology, complex sequences andseries, complex functions, limits, continuity teorlsi 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.

Information on the Institution. Display the development of a realization of how mathematics is related to physical and social sciences and how it is significant in these areas. Perform all phases of life cycle in computer based systems. Describe advanced research methods in the field of Mathematics-Computer Science.

Mapping by elementary functions. Week limits, theorems on limits, limits involving infinity, continuity lompleks. Complex power series ,complex Taylor and Mac-Laurin series and Laurent series,classification of the singular points.

Evaluate advanced knowledge and skills in the field with a critical approach.