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Information
| Code | CMT002 |
| Name | Numerical Methods in Engineering |
| Term | 2024-2025 Academic Year |
| Term | Spring |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | |
| Course Instructor |
1 |
Course Goal / Objective
To teach the numerical methods used in the solution of ordinary and partial differential equations which are encountered in engineering problems and to improve the computer skills of the students.
Course Content
Solution of nonlinear equations, Newton Raphson method, improved Newton-Raphson method, secant method. Numerical solution of nonlinear boundary value problems of ordinary differential equations. Numerical solution of linear and nonlinear partial differential equations; parabolic equations, hyperbolic equations, elliptic equations. Iteration methods. Nonlinear boundary conditions. Two and three dimensional elliptic and parabolic partial differential equations.
Course Precondition
none
Resources
1. Smith, G.D. Numerical Solution of Partial Differential Equations. Clarendon Pres ? Oxford. 2. Chapra, S. C. And Canale R. P. (1998). Numerical Methods for Engineers. Third Edition. McGraw-Hill Book Company.
Notes
Lecture notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | The ability to solve sets of linear equations numerically |
| LO02 | The ability to obtain numerical solutions of ordinary and partial differential equations encountered in engineering problems |
| LO03 | The ability to apply different boundary and initial conditions to numerical solutions |
| LO04 | The ability to develop algorithms required for computer solutions |
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 | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Is equipped with the basic knowledge of math, science and engineering | 5 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Uses computers effectively, has the ability of computer-aided drafting, design, analysis, and presentation | 5 |
| PLO04 | Beceriler - Bilişsel, Uygulamalı | Plans and does experiments in advanced level, interpretes and analizes the results and the data | |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Is equipped with a variety of skills and advanced engineering techniques | 4 |
| 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 | |
| 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 | 3 |
| PLO08 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Identifies a product or its production process, design, development, and prioritise its use | |
| PLO09 | Yetkinlikler - Öğrenme Yetkinliği | Becomes aware of the necessity of lifelong learning and continuously self-renew | 3 |
| PLO10 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Is capable of effective oral and written English for technical or non-technical use | |
| PLO11 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Has teamwork skills, good communication skills and works efficiently as a member of versatile and an interdisciplinary team | 4 |
| PLO12 | Yetkinlikler - Alana Özgü Yetkinlik | Is aware of the technical and ethical responsibilities, inquisitive and innovative |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Introduction to Fourier Series | Lecture Notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 2 | Fourier Series | Lecture Notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 3 | Introduction to Special Functions | Lecture Notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 4 | Special Functions | Lecture Notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 5 | Introduction to Seperation of Variables | Lecture Notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 6 | Seperation of Variables | Lecture Notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 7 | Review | Lecture Notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 8 | Mid-Term Exam | Ölçme Yöntemleri: Yazılı Sınav |
|
| 9 | Introduction to Complex Functions, Complex Integration | Lecture Notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 10 | Complex Functions, Complex Integration | Lecture Notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 11 | Introduction to Residue Theorem | Lecture Notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 12 | Residue Theorem | Lecture Notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 13 | Introduction to Laplace Transform | Lecture Notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 14 | Laplace Transform | Lecture Notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 15 | Complementary Functions Method | Lecture Notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 16 | Term Exams | Ölçme Yöntemleri: Yazılı Sınav |
|
| 17 | Term Exams | 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 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||