Information Package / Course Catalogue
Complex Analysis II
Course Code: MAT302
Course Type: Required
Couse Group: First Cycle (Bachelor's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 2
Prt.: 2
Credit: 3
Lab: 0
ECTS: 6
Objectives of the Course

To make an introduction to complex line integrals, complex series and their prosperities, residues and their applications to various fields.

Course Content

Complex Contour Integral. Cauchy-Goursat Theorems. Cauchy integral formula. Taylor and Laurent series.Uniform Convergence. Classification of singular points. Residue theorem. Argument and Rouche theorems. Applications of Residue theorem to defined integrals.

Name of Lecturer(s)
Lec. Muhammet Ali OKUR
Learning Outcomes
1.Ability to understand the relationship between complex function theory and the theory of functions of a real variable
2.Ability to compute series expansions of analytic functions
3.Ability to make use of integral theorems
4.Ability to classify zeroes and poles of functions and to find out their residues
5.Ability to compute some real improper and trigonometric integrals by making use of Complex analytic methods
Recommended or Required Reading
1.Zill D. G. ve Shanahan P. D., “Kompleks Analiz ve Uygulamaları”, Nobel Akademik Yayıncılık 2013
2.Brown, J. W., Churchill, R. V., “Complex Variables and Applications”, 7th ed. McGraw Hill 2003
3.Spiegel, M. R., “Complex Variables”, SE, Schaum’s Outline Series
4.Başkan T., “Kompleks Fonksiyonlar Teorisi”, Dora Yayıncılık 2012
Weekly Detailed Course Contents
Week 1 - Theoretical & Practice
Complex contour integral
Week 2 - Theoretical & Practice
Simple- and multiply-connected domains, Cauchy-Goursat Theorem, Cauchy-Goursat Theorem for multiply-connected domains
Week 3 - Theoretical & Practice
Independent of path, antiderivative, Cauchy Integral and Derivative Formulas
Week 4 - Theoretical & Practice
Some results of integral theorems, Liouville theorem, Morera Theorem
Week 5 - Theoretical & Practice
Applications related to Cauchy integral formulas
Week 6 - Theoretical & Practice
Complex sequence, Criteria for convergence
Week 7 - Theoretical & Practice
Complex series, Test for divergence, Geometric and telescopic series
Week 8 - Theoretical & Practice
Absolute and conditional convergence, Ratio and root test (Midterm exam)
Week 9 - Theoretical & Practice
Power Series, Radius for convergence, Taylor's Theorem
Week 10 - Theoretical & Practice
Singular points, Laurent series
Week 11 - Theoretical & Practice
Zeros and polars
Week 12 - Theoretical & Practice
Residues
Week 13 - Theoretical & Practice
Cauchy Residues Theorem
Week 14 - Theoretical & Practice
Applications of Cauchy Residues Theorem
Assessment Methods and Criteria
Type of AssessmentCountPercent
Midterm Examination1%40
Final Examination1%60
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory141242
Lecture - Practice141242
Individual Work140228
Midterm Examination118220
Final Examination122224
TOTAL WORKLOAD (hours)156
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
PÇ-16
PÇ-17
PÇ-18
OÇ-1
3
4
4
2
2
OÇ-2
3
4
3
4
2
2
OÇ-3
3
4
3
4
2
2
OÇ-4
3
4
3
4
2
2
OÇ-5
3
4
3
4
2
2
Adnan Menderes University - Information Package / Course Catalogue
2026