TÜRKÇE
ENGLISH
Information
| Code | BBZ208 |
| Name | Numerical Analysis |
| Term | 2024-2025 Academic Year |
| Semester | 4. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Belirsiz |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. GÜZİN YÜKSEL |
| Course Instructor |
1 |
Course Goal / Objective
The aim of this course is to introduce students to various numerical analysis methods and to solve mathematical problems in different fields with numerical analysis methods.
Course Content
In this course, solution methods of linear and non-linear equations (Newton method, Bisection method, Beams method, Bairstow method), Gauss Elimination Method, Gauss-Jordan Elimination Method, Matrix inverse and determinant, Gauss-Siedel Method, Force Method, Interpolation and numerical integral. calculation methods, the least squares method is covered.
Course Precondition
None
Resources
Lee W. Johnson, R. Dean Riess (1982) Numerical Analysis, Addison-Wesley Publishing Company.
Notes
Behiç Çağal (1989), Sayısal Analiz, Seç Yayın Dağıtım, İstanbul.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Make solutions to systems of linear equations. |
| LO02 | Apply Gauss Elimination and Gauss-Jordan Methods for Solving Linear Equations. |
| LO03 | Apply Gauss-Siedel Methods for solving linear equations. |
| LO04 | Finds the root(s) of a function. |
| LO05 | Finds the interpolation polynomial. |
| LO06 | Calculates numerical integrals. |
| LO07 | Examines errors in calculations made. |
| LO08 | Applies the least squares method. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Gain comprehensive knowledge of fundamental concepts, algorithms, and data structures in Computer Science. | 2 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Learn essential computer topics such as software development, programming languages, and database management | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Understand advanced computer fields like data science, artificial intelligence, and machine learning. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Acquire knowledge of topics like computer networks, cybersecurity, and database design. | |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Develop skills in designing, implementing, and analyzing algorithms | 4 |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Gain proficiency in using various programming languages effectively | |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Learn skills in data analysis, database management, and processing large datasets. | |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Acquire practical experience through working on software development projects. | |
| PLO09 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Strengthen teamwork and communication skills. | 3 |
| PLO10 | Yetkinlikler - Alana Özgü Yetkinlik | Foster a mindset open to technological innovations. | 3 |
| PLO11 | Yetkinlikler - Öğrenme Yetkinliği | Encourage the capacity for continuous learning and self-improvement. | 3 |
| PLO12 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Enhance the ability to solve complex problems | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Meaning and Importance of Numerical Analysis, General information about number systems and error. | Reading sources | Öğretim Yöntemleri: Beyin Fırtınası, Tartışma |
| 2 | Bisection and Newton Methods for Solving Non-Linear Equations | Reading sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 3 | Regula-Falsi and Bairstow Methods in Solving Nonlinear Equations | Reading sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 4 | Systems of linear equations, matrix inverse and determinant | Reading sources | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 5 | Gauss Elimination and Gauss-Jordan Methods for Solving Linear Equations | Reading sources | Öğretim Yöntemleri: Tartışma, Anlatım |
| 6 | Gauss Elimination and Gauss-Jordan Methods in Finding Matrix Inverse and Determinant | Reading sources | Öğretim Yöntemleri: Tartışma, Anlatım |
| 7 | Gauss-Seidel Method for Solving Linear Equations | Reading sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 8 | Mid-Term Exam | Written exam | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Interpolation, Linear Interpolation, Lagrange Interpolation | Reading sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 10 | Central difference interpolation | Reading sources | Öğretim Yöntemleri: Soru-Cevap, Anlatım, Tartışma |
| 11 | Forward difference interpolation | Reading sources | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 12 | Backward difference interpolation | Reading sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 13 | Numerical Integral Calculation Methods | Reading sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 14 | Curve fitting, method of least squares | Reading sources | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 15 | Curve fitting, method of least squares 2 | Reading sources | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 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 | 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 | 14 | 14 |
| Final Exam | 1 | 24 | 24 |
| Total Workload (Hour) | 150 | ||
| Total Workload / 25 (h) | 6,00 | ||
| ECTS | 6 ECTS | ||