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Information
| Code | OMZ211 |
| Name | Numerical Analysis |
| Term | 2024-2025 Academic Year |
| Semester | 3. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 4 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Label | C Compulsory |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. ALİ KESKİN |
| Course Instructor |
Dr. Öğr. Üyesi Sibel DOĞRU AKGÖL
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
It is aimed to introduce the language, logic and mathematical operations of numerical methods in engineering science and to provide the application of numerical methods to many scientific, industrial and engineering problems.
Course Content
Introduction to numerical methods; Concept of error in numerical analysis; Solution methods of nonlinear systems of equations; Solution methods of linear systems of equations; Solution methods of eigenvalue problems; Approximate methods; Interpolation; Numerical integration; Numerical differentiation
Course Precondition
There are no prerequisites for the course.
Resources
Richard L. Burden and J. Douglas Faires, Numerical Analysis, Brooks Cole; 7th edition,2000.
Notes
Behiç Çağal, Numerical Analysis, Seç Publishing Distribution, 1st edition, 568pp,1989.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Describes the basic logic of numerical methods. |
| LO02 | Gains the ability to demonstrate the ability to solve engineering problems with the knowledge obtained. |
| LO03 | Selects and applies the appropriate numerical method required to solve a particular problem situation. |
| LO04 | Analyzes sets of linear equations. |
| LO05 | Gain the ability to calculate numerical derivatives and numerical integrals. |
| LO06 | Performs numerical solutions of differential equations. |
| LO07 | Gains the ability to do interpolation. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Applies sufficient knowledge of mathematics, science, and discipline-specific topics in automotive engineering, utilizing theoretical and practical knowledge in solving complex engineering problems. | 3 |
| PLO02 | Beceriler - Bilişsel, Uygulamalı | Identifies, defines, and solves complex engineering problems in automotive engineering applications using scientific methods. | |
| PLO03 | Beceriler - Bilişsel, Uygulamalı | Designs a complex system, process, device, or product in automotive engineering under realistic constraints and conditions to meet specific requirements and effectively applies modern design methods in this process. | |
| PLO04 | Beceriler - Bilişsel, Uygulamalı | Uses information technologies to select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in automotive engineering applications. | |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Designs and conducts experiments, collects data, analyzes, and interprets the results to examine complex engineering problems or discipline-specific research topics in the field of automotive engineering. | |
| PLO06 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Effectively takes responsibility individually and as a team member in intradisciplinary (automotive engineering) and multidisciplinary teams. | |
| PLO07 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Gains knowledge of the legislation related to automotive engineering and awareness of professional ethical responsibility. | |
| PLO08 | Yetkinlikler - Öğrenme Yetkinliği | Being aware of the necessity of lifelong learning and constantly improving and renewing itself in the field of automotive engineering. | |
| PLO09 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Gains the ability to communicate verbally and in writing in Turkish/English regarding the field of automotive engineering, write reports, prepare design and production reports, make effective presentations and use communication technologies. | |
| PLO10 | Yetkinlikler - Alana Özgü Yetkinlik | Using project design and management knowledge, he/she attempts to develop and realize new ideas regarding automotive engineering applications. | |
| PLO11 | Yetkinlikler - Alana Özgü Yetkinlik | Have awareness of the effects of Automotive Engineering applications on health, environment and safety at universal and social dimensions, and the legal consequences of the problems and solutions of the age reflected in the field of automotive engineering. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Introduction, Error concept in numerical methods | Reviewing course notes | Öğretim Yöntemleri: Anlatım |
| 2 | Nonlinear equation system, root of nonlinear equations | Conducting research on the subject | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 3 | Bisection method, Newton Raphson method | Gathering preliminary information about the subject | Öğretim Yöntemleri: Anlatım |
| 4 | Secant method, linear system of equations, direct methods | Review of course notes | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | Gauss Elimination method | Examining the questions in the lecture notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 6 | LU decomposition method | Examining the lecture notes of the relevant section | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 7 | Eigenvalue problems, solution by analytical method | Gathering preliminary information about the subject from lecture notes | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Writing exam | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Force method for the biggest eigenvalue , Force method for the smallest eigenvalue | Review of related book | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | Interpolation | Conducting research on the subject | Öğretim Yöntemleri: Anlatım |
| 11 | Interpolation polinomials | Gathering preliminary information about the subject from literature | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 12 | Numerical Integral, Trapezoidal and Simpson methods | Examining the questions in the lecture notes | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 13 | Gussian Quadrature formulae | Examining the lecture notes of the relevant section | Öğretim Yöntemleri: Anlatım |
| 14 | Numerical Differentiation | Gathering preliminary information about the subject from lecture notes | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 15 | Numerical solutions of Differantial equations | Examining the questions in the book | Öğretim Yöntemleri: Anlatım |
| 16 | Exercises | Examining the questions in the book | Öğretim Yöntemleri: Anlatım |
| 17 | Term Exams | Writing exam | 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 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 7 | 7 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 109 | ||
| Total Workload / 25 (h) | 4,36 | ||
| ECTS | 4 ECTS | ||