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Complex power series ,complex Taylor and Mac-Laurin series and Laurent series,classification of the singular points. Week Final Exam 1st.
Complex Variables and Appliations, author: Giving a series of numbers and fonksiynolar of complex.
theory of complex functions
Week Theoretical Practice Laboratory 1. Liouville’s theorem ,Cauchy’s inequality,essential theorem of algebra,Singularities, zeros and poles. The complex exponential function, logarithms of complexfunction of the complex power function 6. Evaluate and interpret data using the knowledge and skills gained in the fields of mathematics and computer science.
Evaluate advanced knowledge and skills in the field with a critical approach. Be aware of the effects of information applications on individual, institutional, social and universal dimensions and have the awareness about entrepreneurship, innovation. This course covers complex numbers and its basic properties ,topology fonmsiyonlar 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 fonksiyonlat applicationsconform tranformations.
Limits and continuity, differentiation 4. General Information for Students. The complex trigonometric functions 7. Work effectively as an individual and as a team member to solve problems in the areas of mathematics and computer science. Week conformal mapping Series of complex numbers, complex valuedfunctions 3. Fonksiyonlsr 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.
Turkish Course materials in English can be provided to students on demand. Is able to mathematically reorganize, analyze and model problems encountered. Contribution of the Course to Key Learning Outcomes. Cauchy-Riemann equations and analyticity 5.
Classifies singular points of complex functions. Evaluates complex integrals using the residue theorem.
Exponential, logarithmic, trigonometric, hyperbolic, inverse trigonometric functions. Uses effective scientific methods and appropriate technologies to solve problems.
CU Information Package/Course Catalog
Complex hyperbolic functions 8. Exponential, logarithmic, trigonometric and inverse trigonometric functions, Analytic and harmonic functions.
Communicate, mathematical ideas both verbally and in written, making use of numerical, graphical, and symbolic viewpoints. Design and apply interactive experimental environments to get the definitions and first solutions of the problems of computer science and computer science and evaluate these environments.
Recognizes the importance of basic notions in Algebra, Analysis and Topology. Possess the knowledge of advanced research methods in mathematics-computer field.
Kompleks fonksiyonlar teorisi – Necdet San – Google Books
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. Display the development of a realization of how mathematics is related to physical and social sciences and how it is significant in these areas. Complex numbers, complex plane topology, complex sequences andseries, complex functions, limits, fonkssiyonlar and derivatives, Cauchy-Riemannequations, Analytic, complex exponential, logarithmic, trigonometric, andhyperbolic functions, fonksiylnlar 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.
Cauchy-Integral theorem and its consequencesreviews, be analytical functions andseries expansions around some points. Week sufficient conditions for differentiability, polar coordinates 9. Sufficient conditions for derivatives, analytic functions, harmonic functions. Have the awareness of professional and ethical responsibility and legal consequences of information applications Use the knowledge about the field for fonksiyonlaf benefit to society.
Algebra of complex numbers.
Associate’s Degree Short Cycle. Week addition and multiplication, algebraic teroisi, vectors and modules, complex congugate 2.
Determines whether complex functions are analytic. Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. Curves classifies the complex planeintegral accounts. Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
Describe advanced research methods in the field of Mathematics-Computer Science. Week limits, theorems on limits, limits involving infinity, continuity 7.
Face-to-Face Prerequisites and Co-Prerequisites: Finds Taylor and Laurent series of complex functions. Use the time effectively in the process of getting the conclusion with analytical thinking ability.