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Information
| Code | MK575 |
| Name | Analytical Methods in Engineering |
| Term | 2024-2025 Academic Year |
| Semester | . Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | İngilizce |
| Level | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator |
Course Goal / Objective
Demonstrate analytical and series solutions of differential equations.
Course Content
Review of ordinary differential equations (first order ordinary differential equations, second order equations, Euler equation, higher order linear equations; series solution of second order linear equations; solving linear ordinary differential equations by Laplace transform technique). Partial differential equations (Separation of variables technique. Fourier series and the Fourier theorem. Diffusion equation, Wave equation and Laplace's equations). Complex variable theory. Analytic function of a complex variable. Line integrals of complex functions. The calculation of residues. Evaluation of contour integrals by residue theory. Conformal mapping.
Course Precondition
Yok
Resources
Elementary Differential Equations and Boundary Value Problems, 11th Ed., BOYCE, DIPRIMA & MEADE, Wiley
Notes
Elementary Differential Equations and Boundary Value Problems, 11th Ed., BOYCE, DIPRIMA & MEADE, Wiley
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | The student can perform the solution of the ordinary differential equations. |
| LO02 | The student can perform the solution of the partial differential equations. |
| LO03 | The student can perform the solution of the nonlinear differential equations. |
| LO04 | The student can perform the series solution of the differential equations. |
| LO05 | The student can perform the solution of the linear differential equations by the Laplace transformation. |
| LO06 | The student can perform the Fourier series expansion of the differential equations. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Understands and applies basic sciences, mathematics and engineering sciences at a high level. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | He/she has extensive and in-depth knowledge, including the latest developments in his/her field. | 4 |
| PLO03 | Beceriler - Bilişsel, Uygulamalı | They reach the latest information in a field and have a high level of proficiency in the methods and skills necessary to comprehend and research them. | 3 |
| PLO04 | Beceriler - Bilişsel, Uygulamalı | They carry out a comprehensive study that brings innovation to science and technology, develops a new scientific method or technological product/process, or applies a known method to a new field. | 2 |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Independently perceives, designs, implements and concludes an original research process; manages this process. | 2 |
| PLO06 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Contributes to the science and technology literature by publishing the outputs of its academic studies in respected academic environments. | |
| PLO07 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Evaluates scientific, technological, social and cultural developments and conveys them to the society with the awareness of scientific impartiality and ethical responsibility. | |
| PLO08 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Performs critical analysis, synthesis and evaluation of ideas and developments in the field of expertise. | 3 |
| PLO09 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Communicates effectively, both verbally and in writing, with those working in the field of specialization and the wider scientific and social community, communicating and discussing at an advanced level of written, oral and visual communication using a foreign language at least at the C1 General Level of the European Language Portfolio. | |
| PLO10 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Carring out literature survey |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Introduction to Differantial Equations | Study the relevant chapter of the textbook. | Öğretim Yöntemleri: Anlatım |
| 2 | Review of ordinary differential equations, first order ordinary differential equations | Study the relevant chapter of the textbook. | Öğretim Yöntemleri: Anlatım |
| 3 | second order equations | Study the relevant chapter of the textbook. | Öğretim Yöntemleri: Anlatım |
| 4 | Euler equation | Study the relevant chapter of the textbook. | Öğretim Yöntemleri: Anlatım |
| 5 | higher order linear equations | Study the relevant chapter of the textbook. | Öğretim Yöntemleri: Anlatım |
| 6 | series solution of second order linear equations | Study the relevant chapter of the textbook. | Öğretim Yöntemleri: Anlatım |
| 7 | solving linear ordinary differential equations by Laplace transform technique | Study the relevant chapter of the textbook. | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Study the relevant chapter of the textbook. | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Partial differential equations | Study the relevant chapter of the textbook. | Öğretim Yöntemleri: Anlatım |
| 10 | Separation of variables technique. | Study the relevant chapter of the textbook. | Öğretim Yöntemleri: Anlatım |
| 11 | Fourier series and the Fourier theorem. | Study the relevant chapter of the textbook. | Öğretim Yöntemleri: Anlatım |
| 12 | Diffusion equation, Wave equation and Laplace's equations. | Study the relevant chapter of the textbook. | Öğretim Yöntemleri: Anlatım |
| 13 | Complex variable theory. Analytic function of a complex variable. | Study the relevant chapter of the textbook. | Öğretim Yöntemleri: Anlatım |
| 14 | The calculation of residues. Evaluation of contour integrals by residue theory. | Study the relevant chapter of the textbook. | Öğretim Yöntemleri: Anlatım |
| 15 | Conformal mapping. | Study the relevant chapter of the textbook. | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams | Study the relevant chapter of the textbook. | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Study the relevant chapter of the textbook. | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 6 | 84 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 3 | 5 | 15 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 5 | 5 |
| Final Exam | 1 | 8 | 8 |
| Total Workload (Hour) | 154 | ||
| Total Workload / 25 (h) | 6,16 | ||
| ECTS | 6 ECTS | ||