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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 Cauchy-integral 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 : Face-To-Face
Prerequisities and Co-requisities 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", Springer-Verlag New York,1999.
Material Sharing
Documents :
Assignments :
Exams :
Additional Material :
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.
Activity :
Number Duration Total  
Course Duration (Excluding Exam Week) :
14 3 42  
Time Of Studying Out Of Class :
14 4 56  
Homeworks :
10 4 40  
Presentation :
0 0 0  
Project :
0 0 0  
Lab Study :
0 0 0  
Field Study :
0 0 0  
Visas :
1 14 14  
Finals :
1 20 20  
Workload Hour (30) :
30  
Total Work Charge / Hour :
172  
Course's ECTS Credit :
6      
Assessment Methods and Criteria
Studies During Halfterm :
Number Co-Effient
Visa :
1 40
Quiz :
1 10
Homework :
10 40
Attendance :
1 10
Application :
0 0
Lab :
0 0
Project :
0 0
Workshop :
0 0
Seminary :
0 0
Field study :
0 0
   
TOTAL :
100
The ratio of the term to success :
40
The ratio of final to success :
60
TOTAL :
100
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 Cauchy-Riemann 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 Mac-Laurin 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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