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Course Information
Course Unit Title : Complex Variables II
Course Unit Code : MAT306
Type of Course Unit : Compulsory
Level of Course Unit : First Cycle
Year of Study : 3
Semester : 6.Semester
Number of ECTS Credits Allocated : 6,00
Name of Lecturer(s) : ---
Course Assistants :
Learning Outcomes of The Course Unit : Integrals, series, Residues and poles, applications of residues.
Mode of Delivery : Face-To-Face
Prerequisities and Co-requisities Courses : Unavailable
Recommended Optional Programme Components : Unavailable
Course Contents : ntegrals: Contours, Contour integral,antiderivative, Cauchy-Goursat teorem, simply and multiply connected domains, Cauchy integral formula, derivatives of analytic functions, Liouville?s theorem and fundemental theorem of algebra, maximum moduli of functions.
Series: Taylor series, Laurent series, absolute and uniform convergence of power series, integration and differentiation of power series.
Residues and poles: Residue theorems, singular points, zeros and poles of order m.
Applications of residues: Improper integrals, improper integrals involving sines and cosines, definite integrals involving sines and cosines, indented paths.
Languages of Instruction : Turkish-English
Course Goals : To learn contour integrals, Proof of Cauhy Theorems, calculating complex series, calculating integral using residues.
Course Aims : To learn contour integrals, Proof of Cauhy Theorems, calculating complex series, calculating integral using residues.
WorkPlacement   Not Available
Recommended or Required Reading
Textbook : Brawn , J.W., Churchill, R,. ?Complex Variables and its Applications?, McGraw-Hill, 1996
Additional Resources :
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 :
15 4 60  
Homeworks :
3 15 45  
Presentation :
0 0 0  
Project :
0 0 0  
Lab Study :
0 0 0  
Field Study :
0 0 0  
Visas :
1 15 15  
Finals :
1 15 15  
Workload Hour (30) :
30  
Total Work Charge / Hour :
177  
Course's ECTS Credit :
6      
Assessment Methods and Criteria
Studies During Halfterm :
Number Co-Effient
Visa :
1 40
Quiz :
0 0
Homework :
0 0
Attendance :
0 0
Application :
0 0
Lab :
0 0
Project :
0 0
Workshop :
0 0
Seminary :
0 0
Field study :
0 0
   
TOTAL :
40
The ratio of the term to success :
40
The ratio of final to success :
60
TOTAL :
100
Weekly Detailed Course Content
Week Topics  
1 Contours
 
2 Contour integral
 
3 Antiderivative, Cauchy-Goursat theorem
 
4 Simply and multiply connected domains
 
5 Cauchy integral formula, derivatives of analytic functions
 
6 Liouville?s theorem and fundemental theorem of algebra, maximum moduli of functions
 
7 Taylor series, Laurent series,
 
8 Absolute and uniform convergence of power series
 
9 Integration and differentiation of power series
 
10 Residue theorems
 
11 Singular points, zeros and poles of order m
 
12 Improper integrals
 
13 Improper integrals involving sines and cosines,
 
14 Applications of residues