Course Name Code Semester T+U Hours Credit ECTS
Further Complex Analysis I MAT 505 0 3 + 0 3 6
Precondition Courses Advised to take Complex Analysis I-II
Recommended Optional Courses
Course Language Turkish
Course Level yuksek_lisans
Course Type Optional
Course Coordinator Doç.Dr. SELMA ALTUNDAĞ
Course Lecturers Doç.Dr. SELMA ALTUNDAĞ,
Course Assistants
Course Category Field Proper Education
Course Objective The technical applications of complex analysis on engineering,Applications of Taylor and Laurent series,The Argument principle and the Rouche theorem,Conformal mappings(bilinear transformations,tigonometric and fundemental function transformations),Applications of Harmonic functions,The Fourier series and Laplace transformations.
Course Content Complex numbers and functions(main concepts,limit and continuity,branches of functions,differentiable functions,Cauchy-Riemann equations,analytic and harmonic functions),Sequences,Series,Julia and Mandelbrot Sets(fundamental theorems,functions of power series),Complex integral,Taylor and Laurent series(Uniform convergence,isolated points,zeros,poles,applications of Taylor and Laurent series),Residues theorie (calculations of residues,trigonometric integrals,generalised integrals,The Argument principle and the Rouche theorem),The conformal mappings(bilinear transformations,trigonometric and fundamental function transformations),Applications of Harmonic Functions,The Fourier series and Laplace transformations.
# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/she recognizes Taylor and Laurent series. Lecture, Question-Answer, Discussion, Drilland Practice, Simulation, Case Study, Problem Solving, Testing,
2 He/she expresses the Argument principle and the Rouche theorem. Lecture, Question-Answer, Discussion, Drilland Practice, Simulation, Case Study, Problem Solving, Testing,
3 He/she explains the conformal mappings. Lecture, Question-Answer, Discussion, Drilland Practice, Simulation, Case Study, Problem Solving, Testing,
4 He/she interprets the applications of Harmonic functions. Lecture, Question-Answer, Discussion, Drilland Practice, Simulation, Case Study, Problem Solving, Testing,
5 He/she defines the concept of Fourier series. Lecture, Question-Answer, Discussion, Drilland Practice, Simulation, Problem Solving, Testing,
6 He/she applies the Laplace transformations. Lecture, Question-Answer, Discussion, Drilland Practice, Simulation, Problem Solving, Testing,
Week Course Topics Preliminary Preparation
1 Main concepts on complex numbers and functions
2 Limit and continuity,branches of functions,differentiable functions,
3 Cauchy-Riemann equations,analytic and harmonic functions,
4 Sequences,Series,Julia and Mandelbrot Sets
5 The fundamental theorems ,functions of power series
6 Complex integral,Taylor and Laurent series
7 Uniform convergence,isolated points,zeros,poles,applications of Taylor and Laurent series
8 Residues theorie (calculations of residues,trigonometric integrals,generalised integrals
9 Mid term examination
10 The Argument principle and the Rouche theorem
11 The conformal mappings(bilinear transformations,trigonometric and fundamental function transformations),
12 Applications of Harmonic Functions
13 The Fourier series
14 Laplace transformations.
Resources
Course Notes [1] Başarır, Metin; Kompleks Değişkenli Fonksiyonlar Teorisi,Sakarya Kitabevi, 2002,Sakarya.
Course Resources [2] Başkan, Turgut; Kompleks Fonksiyonlar Teorisi,Uludağ Üni.Yay., 1996, Bursa.
[3] Paliouras, John D.; Complex variables for scientist and engineers, Macmillan, 1990, New York
[4] Bak, Joseph, Donald J.Newman; Complex Analysis, Springer-Verlag, 1982.
Order Program Outcomes Level of Contribution
1 2 3 4 5
2 Student follows the current journals in his/her field and puts forward problems. X
2 Student follows the current journals in his/her field and puts forward problems. X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
5 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
5 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
6 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
6 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
7 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
7 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
8 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
8 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
9 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. X
9 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. X
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level.
11 Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. X
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 80
1. Ödev 20
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 20 20
Assignment 2 10 20
Final examination 1 25 25
Total Workload 161
Total Workload / 25 (Hours) 6.44
dersAKTSKredisi 6