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Information
| Code | CMT001 |
| Name | Analytical Methods in Engineering |
| Term | 2024-2025 Academic Year |
| Semester | . Semester |
| Duration (T+A) | 3-1 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3.5 National Credit |
| Teaching Language | Türkçe |
| Level | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Dr. Öğr. Üyesi ENGİN PINAR |
Course Goal / Objective
Equip students with the basic practical information on a variety of engineering mathematics to gain the ability to solve mathematical problems.
Course Content
Ordinary differential equations. Series solutions of ordinary differential equations. Fourier series and Fourier integral. Partial differential equations. Separation of variables. Gamma, Bessel, Laguerre functions.
Course Precondition
non
Resources
İleri Mühendislik Matematiği, Michael D. Greenberg, Prentice Hall, İkinci Baskı
Notes
Lecture notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Finds analytical solutions of linear ordinary and partial differential equations |
| LO02 | Is familiar with Fourier series, and special functions |
| LO03 | Calculate numerical differentiation and integration of functions. |
| LO04 | Find the numerical solution of differential equations. |
| LO05 | Use mathematical methods to solve vector analysis, arithmetic progression and dimensional analysis examples. |
| LO06 | Illustrate the wide-ranging uses of calculus within different construction disciplines by solving problems of differential and integral calculus. |
| LO07 | Investigate applications of statistical techniques to interpret, organise and present data by using appropriate computer software packages |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Is dominated with basic concepts, theories and principles in mechanical engineering | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Is equipped with the basic knowledge of math, science and engineering | 4 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Uses computers effectively, has the ability of computer-aided drafting, design, analysis, and presentation | 2 |
| PLO04 | Beceriler - Bilişsel, Uygulamalı | Plans and does experiments in advanced level, interpretes and analizes the results and the data | 2 |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Is equipped with a variety of skills and advanced engineering techniques | |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | To design a system, component or process in order to meet the needs of various engineering problems within the limitations of technical, economic, environmental, manufacturability, sustainability | 3 |
| PLO07 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Independently reviews and learns the applications in an enterprise, makes a critical assessment of the problems faced with, has the ability of selecting the proper technique to formulate problems and propose solutions | 2 |
| PLO08 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Identifies a product or its production process, design, development, and prioritise its use | 3 |
| PLO09 | Yetkinlikler - Öğrenme Yetkinliği | Becomes aware of the necessity of lifelong learning and continuously self-renew | |
| PLO10 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Is capable of effective oral and written English for technical or non-technical use | 2 |
| PLO11 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Has teamwork skills, good communication skills and works efficiently as a member of versatile and an interdisciplinary team | |
| PLO12 | Yetkinlikler - Alana Özgü Yetkinlik | Is aware of the technical and ethical responsibilities, inquisitive and innovative | 3 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | First Order Differential Equations | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Gösterip Yaptırma, Soru-Cevap |
| 2 | Second Order DE | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Gösterip Yaptırma |
| 3 | Series Solutions of Second Order Linear Equations non homegenuous | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Gösterip Yaptırma |
| 4 | The Laplace Transform | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Gösterip Yaptırma |
| 5 | Systems of First Order Linear Equations | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Gösterip Yaptırma |
| 6 | Nonlinear DE and Stability | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Gösterip Yaptırma |
| 7 | Partial Differential Equations and Fourier Series | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Gösterip Yaptırma |
| 8 | Partial Differential Equations and Weibull distribution Series | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Gösterip Yaptırma |
| 9 | Partial Differential Equations and reighley distribution Series | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Gösterip Yaptırma |
| 10 | Definition of Boundary Value Problems | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Gösterip Yaptırma |
| 11 | Mid-Term Exam | Written Exam | Ölçme Yöntemleri: Yazılı Sınav |
| 12 | Boundary Value Problems | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Gösterip Yaptırma, Anlatım |
| 13 | Solution of Boundary Value Problems | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Gösterip Yaptırma, Anlatım |
| 14 | Numerical Differentiation and Integration | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Gösterip Yaptırma |
| 15 | Curve Fitting Methods | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Gösterip Yaptırma |
| 16 | Term Exams | Written Exam | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Written Exam | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 4 | 56 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 4 | 56 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 1 | 1 | 1 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 28 | 28 |
| Total Workload (Hour) | 153 | ||
| Total Workload / 25 (h) | 6,12 | ||
| ECTS | 6 ECTS | ||