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Week conformal mapping Establishes one-to-one correspondence between real plane and complex numbers. Cauchy-Integral theorem and its consequencesreviews, be analytical fonjsiyonlar andseries expansions around some points. Algebra of complex numbers.

Curves classifies the complex planeintegral accounts. Turkish Course materials in English can be provided to students on demand.

### CU Information Package/Course Catalog

Identify, define and model mathematics, computation and computer science problems; select and apply appropriate analysis and modeling methods for this purpose. Is able to prove Mathematical facts encountered in secondary school. Be aware of the effects of information applications on individual, institutional, social and universal dimensions and have the awareness about entrepreneurship, innovation. Demonstrate in-depth knowledge of mathematics, its scope, application, teoorisi, problems, methods, and usefulness to mankind both as a science and as an intellectual discipline.

MT Course Type: Limits, continuity and differentiability of complex functions. Complex Variables and Appliations, author: Classrooms of Arts and Sciences Faculty.

Contribution of the Course to Key Learning Outcomes. Compulsory Level of Course: Complex hyperbolic functions 8. Giving a series of numbers and series of complex. Classifies singular points of complex functions. Utilize technology as an effective tool in investigating, understanding, and applying mathematics.

## Description of Individual Course Units

Perform all phases of life cycle in computer based systems. Cauchy-Riemann equations and analyticity 5. Develops maturity of mathematical reasoning and writes and develops mathematical proofs.

Finds Taylor and Laurent series of complex functions. Work effectively as an individual and as tdorisi team member to solve problems in the areas of mathematics and computer science.

Gain an in-depth knowledge on Computer Science including computer programming, word processing, database functions, accessing the internet and softwares. Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. 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.

General Information for Students. 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.

Draws mathematical models such as formulas, graphs and tables and explains them. Liouville’s theorem ,Cauchy’s inequality,essential theorem of algebra,Singularities, zeros and poles.

Use the time effectively in the kopmleks of getting the conclusion with analytical thinking ability. Possess the knowledge of advanced research methods in mathematics-computer field. Information on the Institution. Cauchy-Integral theorem and its consequencesreviews, be analytical functions andseries expansions around some points Theory of Complex Functions Course Code: Mapping by elementary functions.

## theory of complex functions

Review of the topics discussed in the lecture notes and sources. Follow current developments about the awareness of the necessity of continuous professional development and information and communication technologies. Series of complex numbers, complex valuedfunctions 3. Display the development of a realization of how fonksiyonlsr is related to physical and social sciences and how it is significant in these areas.

Associate’s Degree Short Cycle. Having the discipline of mathematics, understand the operating logic of the computer and gain the ability to think based on account. 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.

Week polar representation, exponential forms, products and powers in exponential form,arguments of products and quotients 3. Sufficient conditions for derivatives, analytic functions, harmonic functions.

Fonksiyonlzr roots of complex numbers, Euler formula 4. Evaluates some real integrals using complex integration technique. Recognizes the importance of basic notions in Algebra, Analysis and Topology. Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians. Week limits, theorems on limits, limits involving infinity, continuity 7. The complex trigonometric functions 7.

### Complex Analysis I Description | Eskisehir Technical University

Have at least one foreign language knowledge and the ability to communicate effectively in Turkish, verbally and in writing. Evaluates complex integrals using the residue theorem. Exponential, logarithmic, trigonometric, hyperbolic, inverse trigonometric functions.