|Course Title||Code||Semester||L+P Hour||Credits||ECTS|
|Theory of Complex Functions *||MT 334||6||5||5||8|
|Prerequisites and co-requisites|
|Recommended Optional Programme Components||None|
|Language of Instruction||Turkish|
|Course Level||First Cycle Programmes (Bachelor's Degree)|
|Course Coordinator||Prof.Dr. Ali Arslan ÖZKURT|
The aim of this course is to acquaint the student with the theory of the calculus of a function of a complex variable and then to introduce the basic theory and ideas of the integration of a function of a complex variable, state the main theorems such as Cauchy s theorem, Cauchy integral formula, and the Cauchy s residue theorem with endowing the students with practical skills in evaluating real and complex integrals.
Complex numbers, regions, transformations, limit, continuity, differentiation, Cauchy-Riemann equations, Analytic functions, Harmonic functions, elementary transformations, transformations by elementary functions, integrals, contour integrals, Cauchy-Goursattheorem, residue, applications of residue: improper integrals.
|Course's Contribution To Program|
|No||Program Learning Outcomes||Contribution|
Is able to prove Mathematical facts encountered in secondary school.
Recognizes the importance of basic notions in Algebra, Analysis and Topology
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
Is able to express basic theories of mathematics properly and correctly both written and verbally
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
Expresses clearly the relationship between objects while constructing a model
Draws mathematical models such as formulas, graphs and tables and explains them
Is able to mathematically reorganize, analyze and model problems encountered.
Knows at least one computer programming language
Uses effective scientific methods and appropriate technologies to solve problems
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields
Knows programming techniques and is able to write a computer program
Is able to do mathematics both individually and in a group.
|1||Basic properties of comlex numbers, Polar forms, powers, roots, domains||Review of the relevant pages from sources|
|2||Functions of a complex variable, limit and Limit theorems||Review of the relevant pages from sources|
|3||Continuity, derivatives and the Cauchy-Riemann equations||Review of the relevant pages from sources|
|4||Sufficient conditions for derivatives, analytic functions, harmonic functions||Review of the relevant pages from sources|
|5||Exponential, logarithmic, trigonometric, hyperbolic, inverse trigonometric functions||Review of the relevant pages from sources|
|6||Line integrals, upper bound for integrals, anti-derivatives||Review of the relevant pages from sources|
|7||Cauchy-Goursat theorem , Cauchy s integral formula, simply and multiply connected domains||Review of the relevant pages from sources|
|8||Mid-term exam||Review of the topics discussed in the lecture notes and sources|
|9||Taylor and Laurent series||Review of the relevant pages from sources|
|10||sums and product of the series||Review of the relevant pages from sources|
|11||Residues, Cauchy s residue theorem||Review of the relevant pages from sources|
|12||Classification of singular points, residues at poles||Review of the relevant pages from sources|
|13||Applications of residues:evaluation of improper integrals||Review of the relevant pages from sources|
|14||Examples of improper integrals||Review of the relevant pages from sources|
|15||Solving problems||Review of the relevant pages from sources|
|16-17||Final exam||Review of the topics discussed in the lecture notes and sources|
|Recommended or Required Reading|
|Textbook||Complex Variables and Appliations, author: J.W.Brown, R.V. Churchill|
Kompleks Fonksiyonlar Teorisi , author :Turgut Başkan,
Kompleks Değişkenli Fonksiyonlar Teorisi, author:Metin Başarır