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Information
| Code | CEN204 |
| 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 | İngilizce |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. ZEKERİYA TÜFEKCİ |
| Course Instructor |
1 2 |
Course Goal / Objective
To introduce students to techniques for the numerical approximation of mathematical problems, and to the analysis of these techniques.
Course Content
Surveys and applications of numerical techniques related to matrix inversion, systems of linear equations and optimization, finite difference expressions, interpolation and approximation, numerical differentiation and integration.
Course Precondition
no prerequisites
Resources
Numerical Analysis David Kincaid Ward Cheney
Notes
Numerical Analysis Timothy Sauer
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | perform an error analysis for various numerical methods |
| LO02 | Solve an algebraic equation using an appropriate numerical method. |
| LO03 | Solve a linear system of equation using an appropriate numerical method. |
| LO04 | Approximate a function using a numerical method. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Adequate knowledge of mathematics, science and related engineering disciplines; ability to use theoretical and applied knowledge in these fields in solving complex engineering problems. | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Ability to identify, formulate and solve complex engineering problems; ability to select and apply appropriate analysis and modeling methods for this purpose. | 5 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Ability to design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose. | 3 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Ability to select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering practice; ability to use information technologies effectively. | 4 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Ability to design and conduct experiments, collect data, analyze and interpret results to investigate complex engineering problems or discipline-specific research topics. | 2 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Ability to work effectively in interdisciplinary and multidisciplinary teams; individual working skills. | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Ability to communicate effectively verbally and in writing; knowledge of at least one foreign language; ability to write effective reports and understand written reports, prepare design and production reports, make effective presentations, and give and receive clear and understandable instructions. | 2 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Awareness of the necessity of lifelong learning; ability to access information, follow developments in science and technology, and constantly renew oneself. | 4 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Knowledge of ethical principles, professional and ethical responsibility, and standards used in engineering practice. | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Knowledge of business practices such as project management, risk management and change management; awareness of entrepreneurship and innovation; knowledge of sustainable development. | 2 |
| PLO11 | Bilgi - Kuramsal, Olgusal | Knowledge of the effects of engineering practices on health, environment and safety in universal and social dimensions and the problems of the age reflected in the field of engineering; awareness of the legal consequences of engineering solutions. | 3 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Computer arithmetic | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 2 | Floating Point Numbers and Roundoff Errors | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 3 | Absolute and Relative Errors | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 4 | Solutions of nonlinear equations | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 5 | Bisection Method | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 6 | Newton's Method | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 7 | Solutions of linear equations | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 8 | Midterm exam | Ölçme Yöntemleri: Yazılı Sınav |
|
| 9 | Matrix algebra | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 10 | The LU and Cholesky Factorizations | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 11 | Pivoting and Constructing and Algorithm | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 12 | Function approximations | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 13 | Polynomial Interpolation | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 14 | Divided Differences | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 15 | Hermite Interpolation | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 16 | Numerical Differentiation and Integration | Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 17 | Final 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 | ||