Information Package / Course Catalogue
Real and Complex Analysis II
Course Code: MTK502
Course Type: Area Elective
Couse Group: Second Cycle (Master's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 8
Objectives of the Course

This course aims to acquaint students with the fundamental notions of Real and Complex analysis including Fourier transforms, elementary properties of Holomorphic functions, Harmonic functions, the maximum modulus principle, approximation by rational functions, conformal mapping, zeros of holomorphic functions.

Course Content

Fourier transforms, elementary properties of Holomorphic functions, Harmonic functions, the maximum modulus principle, approximation by rational functions, conformal mapping, zeros of holomorphic functions.

Name of Lecturer(s)
Assoc. Prof. Emrah YILDIRIM
Learning Outcomes
1.To be able to comprehend the basic concept of real and complex analysis.
2.To be able to develop mathematical sense
3.To be able to develop the capacity of posing and solving problems
4.To be able to use mathematical concepts in solving certain types of problems
5.To be able to gain the skill of interpreting some interrelations among these concepts
Recommended or Required Reading
1.Real and Complex Analysis, Walter Rudin, 1987.
Weekly Detailed Course Contents
Week 1 - Theoretical
Fourier transforms
Week 2 - Theoretical
Fourier transforms
Week 3 - Theoretical
Fourier transforms
Week 4 - Theoretical
Elementary properties of Holomorphic functions
Week 5 - Theoretical
Elementary properties of Holomorphic functions
Week 6 - Theoretical
Harmonic functions
Week 7 - Theoretical
Harmonic functions
Week 8 - Theoretical
The maximum modulus principle
Week 9 - Theoretical
The maximum modulus principle
Week 10 - Theoretical
Approximation by rational functions (Midterm)
Week 11 - Theoretical
Approximation by rational functions
Week 12 - Theoretical
Conformal mapping, zeros of holomorphic functions
Week 13 - Theoretical
Conformal mapping, zeros of holomorphic functions
Week 14 - Theoretical
Conformal mapping, zeros of holomorphic functions
Assessment Methods and Criteria
Type of AssessmentCountPercent
Midterm Examination1%30
Final Examination1%70
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory140342
Individual Work140684
Midterm Examination130232
Final Examination140242
TOTAL WORKLOAD (hours)200
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
PÇ-12
PÇ-13
PÇ-14
PÇ-15
OÇ-1
4
4
4
4
4
4
4
OÇ-2
4
4
4
4
4
4
4
OÇ-3
4
4
4
4
4
4
4
OÇ-4
4
4
4
4
4
4
4
OÇ-5
4
4
4
4
4
4
4
Adnan Menderes University - Information Package / Course Catalogue
2026