GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
COMPLEX ANALYSIS I/MAT- 407
Course Title: COMPLEX ANALYSIS I
Credits 3 ECTS 5
Semester 7 Compulsory/Elective Elective
COURSE INFO
 -- LANGUAGE OF INSTRUCTION
  Turkish
 -- NAME OF LECTURER(S)
   Assoc.Prof. Hatice Gül 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
To show the Relationship of the complex plane whit IR^2 and their differences
Develop facility with complex numbers and the geometry of the complex plane culminating in finding the n nth roots of a complex number
Show knowledge of whether a complex function is differentiable and use the use the Cauchy-Riemann equations to calculate the derivative
Determine if a function is harmonic and find a harmonic conjugate via the Cauchy-Riemann equations
Understand the similarities and differences between the real and complex exponential function, compute the complex logarithm
Understand the relationships among the exponential, trigonometric and hyperbolic functions, derive simple identities



 -- 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  Definition and Algebraic Properties of Complex Numbers, Geometric Interpretation, Triangle Inequality
2. Week  Polar and Exponential forms of Complex Numbers, Powers and Roots
3. Week  Regions in the complex plane, construction of the complex plane topologie
4. Week   Functions of a complex veriable, limits, theorems on limits, definition of the point at infinity and limits involving the point at infinity
5. Week   Continuous functions, derivatives, differentiation formulas
6. Week  Cauchy-Riemann Equations
7. Week   Analytic functions, harmonic functions
8. Week  Mid-Term Exam
9. Week  The exponential function and its properties
10. Week  Trigonometric functions, hyperbolic functions
11. Week  The logarithmic function and its branches, further properties of logarithms
12. Week  Complex exponenties, inverse trigonometric and hyperbolic functions
13. Week   Mapping by elementary functions, linear functions, the function 1/z
14. Week  Linear fractional transformations and its mappings
15. Week  Mappings of the upper half plane by linear fraction transformations and its appictions
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
 -- 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