| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Analytical Methods I | MEK 503 | 0 | 3 + 0 | 3 | 6 |
| Ön Koşul Dersleri | |
| Önerilen Seçmeli Dersler | |
| Dersin Dili | Türkçe |
| Dersin Seviyesi | YUKSEK_LISANS |
| Dersin Türü | Zorunlu |
| Dersin Koordinatörü | Doç.Dr. ERGÜN NART |
| Dersi Verenler | |
| Dersin Yardımcıları | |
| Dersin Kategorisi | Alanına Uygun Temel Öğretim |
| 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 | The solution methods in mathematical modeling of continuous and discrete systems in engineering are given. The solution of Bessel differential equation and Sturm-Liouville problems in continuous systems are lectured. |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | Students can classify physical systems and problems | Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Homework, |
| 2 | They know generalized mathematical models | Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Homework, |
| 3 | Students turn discrete systems into discrete eigenvalue problems and solve | Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Homework, |
| 4 | They solve differential equation and differential equation systems | Lecture, Question-Answer, Discussion, Drilland Practice, | Testing, Homework, |
| 5 | Students select suitable series and solve differential equations | Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Homework, |
| 6 | They know how to solve Laplace and Bessel differential equations | ||
| 7 | Students know Gamma function and its properties | ||
| 8 | They turn continuous systems into eigenvalue problems | ||
| 9 | Student recognize Sturm-Liouville problem for second order systems and test whether the system is self-adjoint | ||
| 10 | They make eigenvalues and eigenfunction orthogonalzed | ||
| 11 | Students know Nonself-adjoint boundary conditions | ||
| 12 | They know approximate solution techniques for nonself-adjoint eigenvalue problems |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | Classification of physical systems and problems | |
| 2 | Generalized mathematical models | |
| 3 | Discrete eigenvalue problems, properties of eigenvalues & eigenvectors, zero and repeated eigenvalues, iterative methods | |
| 4 | Linear System of ODEs, characteristic eq. , variation of parameters, non-homog. eqs., nonlinear eqs. examples | |
| 5 | Method of Frobenius, Fuchs theorem: series expansion around singular points | |
| 6 | Laplaces eq. in cylindrical coordinates: Solution of Bessels eq., properties of Gamma function, Bessel function of 1st and 2nd kind, modified Bessel functions, applications | |
| 7 | Eigenvalue problems for continuous systems, eigenvalues, eigenfunctions & the solution of initial-boundary problems | |
| 8 | Sturm-Liouville problem for second order systems, general self-adjoint systems, self-adjoint B.C. | |
| 9 | Properties of eigenvalues and eigenfunction, orthogonalization of eigenfunctions | |
| 10 | Midterm exam | |
| 11 | Applications : nonsymetric vibration of circular membrane | |
| 12 | Non-selfadjoint boundary conditions: self-adjoint systems in generalized sense, orthogonality condition, example: vibrating elastic bar with a concentrated mass | |
| 13 | Sturm-Liouville problem for 4th order systems | |
| 14 | Approximate solution of self-adjoint and nonself-adjoint eigenvalue problems, weighted residual techniques. |
| 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 | X | |||||
| 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. | X | |||||
| 6 | Ability to consolidate engineering problems, develop proper method(s) to solve and apply the innovative solutions to them | X | |||||
| 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 | X | |||||
| 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 | 40 |
| 2. Kısa Sınav | 15 |
| 3. Kısa Sınav | 15 |
| 4. Ödev | 30 |
| 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 | 3 | 3 |
| Quiz | 2 | 3 | 6 |
| Assignment | 7 | 5 | 35 |
| Final examination | 1 | 10 | 10 |
| Toplam İş Yükü | 150 | ||
| Toplam İş Yükü / 25 (Saat) | 6 | ||
| Dersin AKTS Kredisi | 6 | ||