GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
COMPLEX ANALYSIS II/MAT- 408
Course Title: COMPLEX ANALYSIS II
Credits 3 ECTS 5
Semester 8 Compulsory/Elective Elective
COURSE INFO
 -- LANGUAGE OF INSTRUCTION
  Turkish
 -- NAME OF LECTURER(S)
   Assoc.Prof. H.Gül İNCE İLARSLAN, Assoc.Prof. Cüneyt ÇEVİK
 -- WEB SITE(S) OF LECTURER(S)
  websitem.gazi.edu.tr/site/ince, websitem.gazi.edu.tr/site/ccevik
 -- EMAIL(S) OF LECTURER(S)
  ince@gazi.edu.tr, ccevik@gazi.edu.tr
 -- LEARNING OUTCOMES OF THE COURSE UNIT
Representation of each analytic function with an unique power series, usefulness of some complex integrals in evaluating of some real integrals
Determine whether a complex series converges, show understanding of the region of convergence for power series
Set up and directly evaluate contour integrals
Identify when the theorems are applicable and evaluate contour integrals using the Cauchy Integral Formula in basic and extended form
Find Taylor or Laurent Series for simple function, show the convergence regions for each type of series
Identify and classify zeros and singular points of functions
Compute residues, use residues to evaluate various contour integrals


 -- 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  Integrations of comple-valued functions of real variable
2. Week  Contours and contour integrals
3. Week  Antiderivatives and Cauchy-Goursat Theorem, Integrals on simply and multiply connected domains
4. Week   Cauchy Integral Formula, derivatives of analytic functions, Morera’s Theorem
5. Week   Maximum Moduli Theorem, Liouville’s Theorem and The Fundemental Theorem of Algebra
6. Week  Sequence and series of functions and uniform convergence
7. Week  Complex Taylor and Maclaurin series
8. Week  Mid-Term Exam
9. Week  Laurent series
10. Week   Uniqueness of series representations, multiplication and division of power series
11. Week  Classification of the singular points
12. Week  Calculation of Residue
13. Week  Residue theorem
14. Week  Calculation of some real integrals with complex methods
15. Week   Calculation of improper integrals involving sines and cosines and definite integrals involving sines and cosines with complex methods
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 ;M.Başarır,Kompleks Değişkenli Fonksiyonlar Teorisi
 -- PLANNED LEARNING ACTIVITIES AND TEACHING METHODS
  Lecture, Question-Answer, Demonstration, Drill-Practise -- STAJ / UYGULAMA (WORK PLACEMENT(S)) -- Maks. Karakter: 150
 -- WORK PLACEMENT(S)
  None
 -- 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
0
0
0
 Reading
5
4
20
 Searching in Internet and Library
6
5
30
 Designing and Applying Materials
0
0
0
 Preparing Reports
0
0
0
 Preparing Presentation
0
0
0
 Presentation
0
0
0
 Mid-Term and Studying for Mid-Term
1
14
14
 Final and Studying for Final
1
28
28
 Other
0
 TOTAL WORKLOAD: 
134
 TOTAL WORKLOAD / 25: 
5.36
 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 give good education in the program fields as algebra, geometry, applied mathematics, topology and analysis in order to be equipped with enough mathematics.X
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
10To enable the student to gain the ability of relating mathematics with the other sciences.X