| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Analytic Methods II | MEK 602 | 0 | 3 + 0 | 3 | 6 |
| Ön Koşul Dersleri | |
| Önerilen Seçmeli Dersler | |
| Dersin Dili | Türkçe |
| Dersin Seviyesi | Doktora |
| Dersin Türü | Seçmeli |
| Dersin Koordinatörü | Doç.Dr. ERGÜN NART |
| Dersi Verenler | |
| Dersin Yardımcıları | |
| Dersin Kategorisi | Diğer |
| Dersin Amacı | The main aim is to teach students the theory of Advanced Analytical Methods and have them solve various examples from Mechanical engineering |
| Dersin İçeriği | It contains analytical solution methods in engineering mathematics. It starts with variational calculus, continue with complex functions, and finishes with Hilbert transformations. |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | Students know the main idea of variational calculus | Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Homework, |
| 2 | They apply variational calculus in mechanical problems | Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Homework, |
| 3 | Student know definitions, introduction, multivalued functions of complex variables | Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Homework, |
| 4 | They take derivatives of complex variable functions and test Cauchy-Riemann conditions | Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Homework, |
| 5 | Students find Laurent series for functions | Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Homework, |
| 6 | They calculate infinite integrals | Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Homework, |
| 7 | Students know partial differential equations and the solution techniques, and apply boundary conditions | Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Homework, |
| 8 | They know integral transformations | Problem Solving, Lecture, Question-Answer, Discussion, Drilland Practice, | Testing, Homework, |
| 9 | Students apply Laplace transformation to engineering problems | Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Homework, |
| 10 | They apply Mellin transformation to engineering problems | Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Homework, |
| 11 | Students apply Henkel transformation to engineering problems | Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Homework, |
| 12 | They apply Hilbert transformation to engineering problems | Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Homework, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | Variational Calculus | |
| 2 | Complex Variables : Definitions, introduction, multivalued functions | |
| 3 | Derivatives, Analytic Functions, Cauchy-Riemann Conditions | |
| 4 | Laurent series, Residues, simple and multiple poles, examples : contour integrals, evaluation of some real definite integrals | |
| 5 | Infinite integrals, examples : Fourier integrals, branch cuts | |
| 6 | Partial Differential Equations ( unbounded domain ) | |
| 7 | Characteristic equation, example : the wave equations, continuous eigenvalues : Fourier series to Fourier integrals | |
| 8 | Integral Transforms | |
| 9 | Initial Value Problems Laplace Transform | |
| 10 | Midterm exam | |
| 11 | Boundary Value Problems in Polar Coord. Mellin Transforms | |
| 12 | Integral Equations | |
| 13 | Boundary Value Problems in cylindrical coord. Hankel Transform | |
| 14 | Hibert Transforms |
| Kaynaklar | |
|---|---|
| Ders Notu | F.B. Hildebrand, Advanced Calculus for Applications 2nd Edition, Prentice-Hall, Inc. F.B. Hildebrand, Methods of Applied Mathematics, Dover Publications, Inc. |
| Ders Kaynakları | C.R. Wylie, L.C. Barrett, Advanced Engineering Mathematics, McGraw-Hill Book Company |
| Sıra | Program Çıktıları | Katkı Düzeyi | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Ability to access wide and deep information with scientific researches in the field of Engineering, evaluate, interpret and implement the knowledge gained in his/her field of study | ||||||
| 2 | Develop new strategic approach and produce solutions by taking responsibility in unexpected and complicated situations in mechatronic engineering | ||||||
| 3 | Aware of social, scientific and ethical values guarding adequacy at all professional activities and at the stage of data collection, interpretation, and announcement | ||||||
| 4 | Develop and use data processing and communication technologies together with the machine, electronic and computer software-hardware knowledge required by the field of mechatronic engineering expertise | ||||||
| 5 | Ability to complete and implement "limited or incomplete data" by using the scientific methods. | ||||||
| 6 | Ability to consolidate engineering problems, develop proper method(s) to solve and apply the innovative solutions to them | ||||||
| 7 | Ability to develop new and original ideas and method(s), to develop new innovative solutions at design of system, component or process | ||||||
| 8 | Ability to design and apply analytical, modeling and experimental based research, analyze and interpret the faced complex issues during the design and apply process | ||||||
| 9 | Gain high level ability to define the required information and data | ||||||
| 10 | Aware of new and developing application of profession and ability to analyze and study on those applications | ||||||
| 11 | Ability to interpret engineering applications social and environmental dimensions and it´s compliance with the social environment | ||||||
| 12 | At least be capable of oral and written communication in a foreign language | ||||||
| 13 | Ability to work in multi-disciplinary teams and to take responsibility to define approaches for complex situations | ||||||
| 14 | Systematic and clear verbal or written transfer of the process and results of studies at national and international environments | ||||||
| 15 | Gain comprehensive information on modern techniques, methods and their borders which are being applied to engineering | ||||||
| Değerlendirme Sistemi | |
|---|---|
| Yarıyıl Çalışmaları | Katkı Oranı |
| 1. Ara Sınav | 45 |
| 1. Kısa Sınav | 15 |
| 1. Ödev | 2 |
| 1. Proje / Tasarım | 10 |
| 2. Kısa Sınav | 15 |
| 2. Ödev | 2 |
| 3. Ödev | 2 |
| 4. Ödev | 2 |
| 5. Ödev | 2 |
| 6. Ödev | 2 |
| 7. Ödev | 3 |
| Toplam | 100 |
| 1. Yıl İçinin Başarıya | 40 |
| 1. Final | 60 |
| 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 | 4 | 4 |
| Quiz | 2 | 5 | 10 |
| Assignment | 7 | 5 | 35 |
| Project / Design | 1 | 5 | 5 |
| Final examination | 1 | 10 | 10 |
| Toplam İş Yükü | 160 | ||
| Toplam İş Yükü / 25 (Saat) | 6,4 | ||
| Dersin AKTS Kredisi | 6 | ||