Rapor Tarihi: 13.04.2026 03:08
| Course Title | Code | Language | Type | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| Numerical Analysis I | MAT307 | Turkish | Compulsory | 5. Semester | 2 + 2 | 3.0 | 5.0 |
| Prerequisite Courses | |
| Course Level | Undergraduate |
| Mode of delivery | Lecturing |
| Course Coordinator | Prof. Dr. FUAT USTA |
| Instructor(s) | |
| Goals | To provide students the ability of using computers to solve numerical problems and to emphasize the importance of error analysis. |
| Course Content | Binary Number System; Error analysis; Solving the equation x = g(x): Fixed-point iteration; Newton method for nonlinear system; Solutions of linear system equations; Lagrange and Newton polynomials; polinomial approximation; Numerical diferentiation, integration and Optimization; Numerical solutions of initial and boundary value problems. |
| # | Öğrenme Kazanımı |
| 1 | The students gain primary informations about the mathematics |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | Binary Number System | |
| 2. Week | Error analysis | |
| 3. Week | Soltions of x= g(x), Fixed-Point Iteration, Creep Method, Newton-Raphson and Beam Methods | |
| 4. Week | Aitken’s Process, Steffensen’s and Muller’s Methods | |
| 5. Week | Iterations for Nonlinear Systems | |
| 6. Week | Newton’s Method for Nonlinear Systems | |
| 7. Week | Solutions of systems of linear equations: Gaussian Elimination and LU decomposition | |
| 8. Week | Mid-term Exam | |
| 9. Week | Lagrange Polynomıals | |
| 10. Week | Newton Polynomials and Polynomial Approximation | |
| 11. Week | Least Squares Method, Curve Fitting | |
| 12. Week | Numerical Differentiation and Numerical Integration | |
| 13. Week | Numerical Optimization | |
| 14. Week | Numerical Solutions of Initial and Boundary Value Problems: Euler, Heun, Taylor and Runge-Kutta Methods |
| No | Program Requirements | Level of Contribution | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Possesses theoretical and applied knowledge of the fundamental areas of mathematics (Analysis and Function Theory, Algebra and Number Theory, Geometry, Applied Mathematics, Topology and Foundations of Mathematics, and Mathematical Logic). | ✔ | |||||
| 2 | Explains the historical development of mathematical concepts, their relationship with other branches of science, and their application areas. | ✔ | |||||
| 3 | Defines mathematical problems, selects appropriate methods, and solves them using analytical/numerical techniques. | ✔ | |||||
| 4 | Constructs mathematical expressions with logical integrity and reaches conclusions using proof methods. | ✔ | |||||
| 5 | Formulates and interprets real-life problems by performing mathematical modeling. | ✔ | |||||
| 6 | Effectively uses information technologies and mathematical software in data analysis and computation processes. | ||||||
| 7 | Takes responsibility in individual or team work; plans and executes projects. | ✔ | |||||
| 8 | Follows current developments in their field; improves themselves with a lifelong learning awareness. | ✔ | |||||
| 9 | Expresses mathematical ideas verbally and in writing clearly and in accordance with academic rules. | ✔ | |||||
| 10 | Acts in accordance with professional and academic ethical values; acts with a sense of social responsibility. | ✔ | |||||
| Program Requirements | DK1 |
|---|---|
| PY1 | 4 |
| PY2 | 5 |
| PY3 | 4 |
| PY4 | 4 |
| PY5 | 1 |
| PY6 | 0 |
| PY7 | 5 |
| PY8 | 5 |
| PY9 | 3 |
| PY10 | 4 |
| PY11 | 1 |
| PY12 | 5 |
| PY13 | 4 |
| PY14 | 4 |
| PY15 | 4 |
| Ders Kitabı veya Notu | Ders Kitabı veya Ders Notu bulunmamaktadır. |
|---|---|
| Diğer Kaynaklar |
|
| ECTS credits and course workload | Quantity | Duration (Hour) | Total Workload (Hour) | |
|---|---|---|---|---|
|
Ders İçi |
Class Hours | 13 | 4 | 52 |
|
Sınavlar |
Midterm | 1 | 2 | 2 |
| Homework | 14 | 2 | 28 | |
| Homework Preparation | 14 | 1 | 14 | |
| Final | 1 | 2 | 2 | |
| Practice | 14 | 1 | 14 | |
| Practice End-Of-Term | 14 | 1 | 14 | |
| Classroom Activities | 14 | 2 | 28 | |
| Total Workload | 154 | |||
| *AKTS = (Total Workload) / 25,5 | ECTS Credit of the Course | 5.0 | ||
