GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
COMPLEX ANALYSIS II/MAT3004
Course Title: COMPLEX ANALYSIS II
Credits 4 ECTS 5
Semester 6 Compulsory/Elective Compulsory
COURSE INFO
 -- LANGUAGE OF INSTRUCTION
   Turkish
 -- NAME OF LECTURER(S)
  Asist. Prof. Kadir KANAT
 -- WEB SITE(S) OF LECTURER(S)
  http://www.websitem.gazi.edu.tr/site/kadirkanat
 -- EMAIL(S) OF LECTURER(S)
  kadirkanat@gazi.edu.tr
 -- LEARNING OUTCOMES OF THE COURSE UNIT
He/she knows definition of contour and its properties and can make contour integral calculations.
He/she solves problems with integrals defined on simple and very connected regions.
He/she knows different kinds of series defined in the complex plane and the features they provide.
He/she can do integral calculus in the complex plane.
He/she learns subjects about integral along a branch cut,Inverse Laplace transform,logarithmic residues and Rouche Theorem.
He/she can do conformal transformations.
 -- MODE OF DELIVERY
  The mode of delivery of this course is Face to face
 -- PREREQUISITES AND CO-REQUISITES
  There is no prerequisite or co-requisite for this course.
 -- RECOMMENDED OPTIONAL PROGRAMME COMPONENTS
  There is no recommended optional programme component for this course.
 --COURSE CONTENT
1. Week  The images and regions of transformations made with w=expz,logarithm,w=sinz,w=z^2,w=z^(1/2) functions
2. Week   Contours and contour integrals
3. Week  Primitives and Cauchy-Goursat theorem,integrals defined on simple and very connected regions
4. Week  Cauchy Integral Formula,derivatives of analytic functions, Morera theorem
5. Week   Maximum Modulus Theorem, Liouville theorem and The Fundamental Theorem of Algebra
6. Week   Taylor and Laurent series
7. Week   Absolute and uniform convergence of power series,integration and derivatives of power series
8. Week  Midterm exam
9. Week  Uniqueness of representation of series,multiplication and division of power series
10. Week   Residue Theorem,principal part of a function, residues at the poles
11. Week  m-th and zero order pole locations of afunction
12. Week  Account of generalized real integrals,generalized integrals containing the sine and cosine functions and definite integrals
13. Week   Integral along a branch cut,Inverse Laplace transform,logarithmic residues and Rouche Theorem
14. Week  Protection of angles and conformal transformations
15. Week   Analytic continuation and reflection principles, Schwarz-Christoffel dönüşümü
16. Week  Final exam
 -- RECOMMENDED OR REQUIRED READING
   R.V.Churchill and J.W.Brown, Complex Variables and Applications; M.R.Spiegel,Complex Variables; T.Başkan, Kompleks Fonksiyonlar Teorisi
 -- PLANNED LEARNING ACTIVITIES AND TEACHING METHODS
  Lecture, Question & Answer, Demonstration, Drill - Practise
 -- WORK PLACEMENT(S)
  Not Applicable
 -- ASSESSMENT METHODS AND CRITERIA
 
Quantity
Percentage
 Mid-terms
1
40
 Assignment
0
0
 Exercises
0
0
 Projects
0
0
 Practice
0
0
 Quiz
0
0
 Contribution of In-term Studies to Overall Grade  
40
 Contribution of Final Examination to Overall Grade  
60
 -- WORKLOAD
 Efficiency  Total Week Count  Weekly Duration (in hour)  Total Workload in Semester
 Theoretical Study Hours of Course Per Week
14
3
42
 Practising Hours of Course Per Week
14
2
28
 Reading
0
 Searching in Internet and Library
5
2
10
 Designing and Applying Materials
0
 Preparing Reports
0
 Preparing Presentation
0
 Presentation
0
 Mid-Term and Studying for Mid-Term
6
2
12
 Final and Studying for Final
8
2
16
 Other
11
2
22
 TOTAL WORKLOAD: 
130
 TOTAL WORKLOAD / 25: 
5.2
 ECTS: 
5
 -- COURSE'S CONTRIBUTION TO PROGRAM
NO
 PROGRAM LEARNING OUTCOMES
1
2
3
4
5
1To train individuals who are contemporary, entrepreneur and have unique and aesthetic values, self-confidence and capable of independent decision-making.X
2To train individuals who are equipped with enough mathematicsX
3To teach mathematical thinking methods in order to improve the ability to express mathematics both orally and in writing,X
4To train individuals who are knowledgeable about the history of mathematics and the production of scientific knowledge and can follow developments in these disciplines.X
5To provide necessary equipments to take positions such areas as banking, finance, econometrics, and actuarial,X
6To acquire ability to solve problems encountered in real life by means of mathematical modeling using mathematical methods,X
7To provide ability to do necessary resource researches in the areas of mathematics and to use accessed information,X
8To give appropriate training in such areas as in computer programming and creating algorithms in order to take parts in developing IT sector,X
9To gain substructure to be able to study at graduate level.X
10The skill to have professional and ethical responsibilityX