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COURSE INFORMATON
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 Type
Course Coordinator Prof.Dr. Ali Arslan ÖZKURT
Instructors
 Prof.Dr. DOĞAN DÖNMEZ 1. Öğretim Grup:A Prof.Dr. DOĞAN DÖNMEZ 2. Öğretim Grup:A

Assistants
Goals
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.
Content
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.

Learning Outcomes
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Course's Contribution To Program
NoProgram Learning OutcomesContribution
12345
1
Is able to prove Mathematical facts encountered in secondary school.
X
2
Recognizes the importance of basic notions in Algebra, Analysis and Topology
X
3
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
X
4
Is able to express basic theories of mathematics properly and correctly both written and verbally
X
5
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
X
6
Expresses clearly the relationship between objects while constructing a model
X
7
Draws mathematical models such as formulas, graphs and tables and explains them
X
8
Is able to mathematically reorganize, analyze and model problems encountered.
X
9
Knows at least one computer programming language
10
Uses effective scientific methods and appropriate technologies to solve problems
X
11
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
12
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
13
Knows programming techniques and is able to write a computer program
14
Is able to do mathematics both individually and in a group.
X

Course Content
WeekTopicsStudy Materials _ocw_rs_drs_yontem
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