

Course Information
Course Unit Title 
: 
Complex Analysis and Applications 
Course Unit Code 
: 
01IMM5121 
Type of Course Unit 
: 
Optional 
Level of Course Unit

: 
Second Cycle 
Year of Study

: 
Preb 
Semester

: 
255.Semester 
Number of ECTS Credits Allocated

: 
6,00 
Name of Lecturer(s) 
: 


Course Assistants 
: 

Learning Outcomes of The Course Unit 
: 
1) To be able to understand the relationship between the complex and real numbers. 2) Concepts of sequence and series in complex number 3) To be able to apply the limit, continuity and the complex differentation 4) To be able to interpretation of analytic function concept 5) To be able to calculate an integral on complex plane 6) To undestand Cauchyintegral theorem 7) To be able to use series expansions of functions 8) To classify of the singular points 9) To be able to apply Residue theorem and calculation of some real

Mode of Delivery 
: 
FaceToFace

Prerequisities and Corequisities Courses 
: 
Unavailable

Recommended Optional Programme Components 
: 
Unavailable

Course Contents 
: 
Complex number, Complex variable, Complex functions, derivative and integrals of complex functions, Cauchy integral theorems, Laurent series, singular points of analytical functions, residue calculationn, Cauchy residue theorems

Languages of Instruction 
: 
Turkish

Course Goals 
: 
1) To understand the main properties and examples of complex numbers and functions 2) To be able to compute and manipulate series expansions for analytic functions; 3) To know and be able to use the major integral theorems for complex analysis 4) To understand the relationship between complex function theory and the real function theory 5) To understand Singular points and residue theorems

Course Aims 
: 
To learn fundamental concepts and calculations of complex functions theory for analysis of engineering problems

WorkPlacement 

Not Available


Recommended or Required Reading
Textbook

: 

Additional Resources

: 
Cohen, Harold. "Fundamentals and applications of complex analysis", Kluwer Academic / Plenum Publi New York, 1998.
Junjiro, Noguchi. "Introduction to complex analysis", American Mathematical Society Rhode Island, 1998 .
Priestley, H.A. "Introduction to complex analysis", Oxford University Pres , 1990.
Saff, E. B. "Fundamentals of complex analysis with applications for engineering", Prentice Hall New Jersey, 2003.
Shakarchi, Rami. "Problems and solutions for complex analysis", SpringerVerlag New York,1999.

Material Sharing
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Exams

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Planned Learning Activities and Teaching Methods
Lectures, Practical Courses, Presentation, Seminar, Project, Laboratory Applications (if necessary)


ECTS / Table Of Workload (Number of ECTS credits allocated)
Student workload surveys utilized to determine ECTS credits.

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Workload Hour (30)

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Assessment Methods and Criteria
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Visa

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Weekly Detailed Course Content
Week

Topics

1

Complex numbers and properties


Study Materials: To investigate required sources

2

Sequence and series in complex numbers


Study Materials: To investigate required sources

3

Complex valued functions


Study Materials: To investigate required sources

4

Limit, continuity and differentiation in complex functions


Study Materials: To investigate required sources

5

CauchyRiemann equations and complex functions


Study Materials: To investigate required sources

6

İntegrals of complex valued functions


Study Materials: To investigate required sources

7

Contours and contours integrals


Study Materials: To investigate required sources

8

Sample applications


Study Materials: To investigate required sources

9

Complex Taylor and MacLaurin series


Study Materials: To investigate required sources

10

Laurent series


Study Materials: To investigate required sources

11

Classification of singular points


Study Materials: To investigate required sources

12

Calculation of Residue


Study Materials: To investigate required sources

13

Calculation of some real integrals in complex functions


Study Materials: To investigate required sources

14

Sample applications


Study Materials: To investigate required sources

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