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Information
| Code | ISB301 |
| Name | Numerical Analysis |
| Term | 2024-2025 Academic Year |
| Semester | 5. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. SADULLAH SAKALLIOĞLU |
| Course Instructor |
Doç. Dr. NİMET ÖZBAY
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The aim of this course is to introduce various methods of numerical analysis to students and to make solutions of mathematical problems in different fields with numerical analysis methods.
Course Content
The content of this course consists of the following topics: Solution methods of linear and nonlinear equations (Newton's method, Bisection method, Bairstow method), Gaussian Elimination Method, Gauss-Jordan Elimination Method, Inverse and determinant of matrix, Gauss-Siedel Method, Interpolation and numerical integral methods The least squares method.
Course Precondition
Lineer Eşitliklerin Çözümünde Gauss-Seidel Yöntemini uygulayabilmesi,
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 | Find Root of a function |
| LO05 | Find polynomial interpolation, |
| LO06 | Use to approximate definite integrals |
| LO07 | Examines errors in calculations |
| LO08 | Apply least squares method |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Explain the essence fundamentals and concepts in the field of Statistics | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Emphasize the importance of Statistics in life | 2 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Define basic principles and concepts in the field of Law and Economics | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Produce numeric and statistical solutions in order to overcome the problems | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Use proper methods and techniques to gather and/or to arrange the data | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Utilize computer programs and builds models, solves problems, does analyses and comments about problems concerning randomization | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Apply the statistical analyze methods | 2 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Make statistical inference (estimation, hypothesis tests etc.) | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Generate solutions for the problems in other disciplines by using statistical techniques and gain insight | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Discover the visual, database and web programming techniques and posses the ability of writing programs | |
| PLO11 | Beceriler - Bilişsel, Uygulamalı | Distinguish the difference between the statistical methods | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Make oral and visual presentation for the results of statistical methods | |
| PLO13 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Have capability on effective and productive work in a group and individually | 4 |
| PLO14 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Professional development in accordance with their interests and abilities, as well as the scientific, cultural, artistic and social fields, constantly improve themselves by identifying training needs | 2 |
| PLO15 | Yetkinlikler - Öğrenme Yetkinliği | Develop scientific and ethical values in the fields of statistics-and scientific data collection |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Meaning of numerical analysis, number systems, and general information about the error, | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 2 | Methods of Solving Nonlinear Equations; bisection and Newton methods | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 3 | Methods of Solving Nonlinear Equations, Regula-Falsi and Bairstow methods, | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 4 | Systems of linear equations, matrix inverse and determinant | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 5 | Solving Linear Equations; Gauss Elimination and Gauss-Jordan Methods | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 6 | Gauss Elimination and Gauss-Jordan Methods for finding inverse of the matrix and determinant. | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 7 | Gauss-Seidel Method of Solving Linear Equations | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 8 | Mid-Term Exam | Written Exam | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Interpolation, linear interpolation, Lagrange Interpolation | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 10 | Central difference interpolation | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 11 | Forward difference interpolation | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 12 | Backward difference interpolation | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 13 | Numerical integration methods | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 14 | Curve fitting, method of least squares | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 15 | Curve fitting, method of least squares 2 | Source reading | Öğretim Yöntemleri: Anlatım, Tartışma, 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 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||