| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Further Complex Analysıs I | MAT 505 | 0 | 3 + 0 | 3 | 6 |
| Ön Koşul Dersleri | Advised to take Complex Analysis I-II |
| Önerilen Seçmeli Dersler | |
| Dersin Dili | Türkçe |
| Dersin Seviyesi | YUKSEK_LISANS |
| Dersin Türü | Seçmeli |
| Dersin Koordinatörü | Doç.Dr. AYNUR ŞAHİN |
| Dersi Verenler | Prof.Dr. SELMA ALTUNDAĞ, |
| Dersin Yardımcıları | |
| Dersin Kategorisi | Alanına Uygun Öğretim |
| Dersin Amacı | 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. |
| Dersin İçeriği | 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. |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 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, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 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. |
| Kaynaklar | |
|---|---|
| Ders Notu | [1] Başarır, Metin; Kompleks Değişkenli Fonksiyonlar Teorisi,Sakarya Kitabevi, 2002,Sakarya. |
| Ders Kaynakları | [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. |
| Sıra | Program Çıktıları | Katkı Düzeyi | |||||
|---|---|---|---|---|---|---|---|
| 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 | |||||
| Değerlendirme Sistemi | |
|---|---|
| Yarıyıl Çalışmaları | Katkı Oranı |
| 1. Ara Sınav | 80 |
| 1. Ödev | 20 |
| Toplam | 100 |
| 1. Yıl İçinin Başarıya | 50 |
| 1. Final | 50 |
| Toplam | 100 |
| AKTS - İş Yükü Etkinlik | Sayı | Süre (Saat) | Toplam İş Yükü (Saat) |
|---|---|---|---|
| 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 |
| Toplam İş Yükü | 161 | ||
| Toplam İş Yükü / 25 (Saat) | 6,44 | ||
| Dersin AKTS Kredisi | 6 | ||