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| MATI5033 | Numerical Methods | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Second Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Doç. Dr. Pelin ŞENEL | | Co-Lecturer | Prof. Selçuk Han Aydın | | Language of instruction | | | Professional practise ( internship ) | None | | | | The aim of the course: | | To demonstrate derivation, application, convergence, and stability conditions of basic numerical analysis techniques that are utilized in Engineering and Mathematics research. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | Examine the need of numerical approximation for mathematical or engineering problems. | 1,2,3,4 | 1,3, | | PO - 2 : | Apply suitable numerical techniques to problems. | 1,2,3,4 | 1,3, | | PO - 3 : | Carry out error, convergence and stability analysis. | 1,2,3,4 | 1,3, | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| Numerical approximation, error types. Numerical solutions of linear systems (Gaussian elimination, LU decomposition, Jacobi, Gauss-Seidel, SOR and least-squares methods, QR and SVD decompositions). Numerical solutions of eigen value and eigenvector problems (power, inverse power, and Rayleigh quotient methods). Numerical solutions of root finding problems (Newton and secant methods, fixed point iteration). Interpolation (polynomial and spline interpolations). Numerical differentiation (Taylor series approximation formulas, Richardson extrapolation). Numerical integration (rectangular, trapezoidal, and Simpson's methods, Newton and Gauss integration formulas).
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Introduction to numerical methods and error types. Convergence and stability analysis. | | | Week 2 | Linear system of equations, matrix-vector analysis. | | | Week 3 | Direct methods (Gauss elimination and LU factorization). | | | Week 4 | Iterative methods (Jacobi, Gauss-Seidel methods), Successive-Over-Relaxation (SOR) method. | | | Week 5 | Least-squares method, QR and SVD decompositions. | | | Week 6 | Eigenvalue and eigenvector problems (power and inverse power methods, Rayleigh Quotient method). | | | Week 7 | Root finding problems (Newton and secant methods). | | | Week 8 | Fixed point iteration, Newton method for system of equations. | | | Week 9 | Midterm exam | | | Week 10 | Interpolation (Polynomial and spline interpolations). | | | Week 11 | Numerical differentiation (Taylor series approximations, Richardson extrapolation). | | | Week 12 | Numerical integration (Rectangular and trapezoidal methods). Midterm exam. | | | Week 13 | Simpson method. | | | Week 14 | Newton and Gauss methods. | | | Week 15 | Multiple integrations. | | | Week 16 | Final Exam. | | | |
| 1 | Burden, R.L., Faires, J.D. 2011; Numerical Analysis, Brooks/Cole Cengage Learning, Boston. | | | 2 | Tezer-Sezgin M, Bozkaya C. 2018; Numerical Analysis, ODTÜ, Ankara. | | | |
| 1 | Kincaid, D., Cheney, W. 1991; Numerical Analysis Mathematics of Scientific Computing, Brooks/Cole, California. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 20.11.2024 | 2 | 30 | | Homework/Assignment/Term-paper | 12 | 11.12.2024 | 2 | 20 | | End-of-term exam | 16 | 15.01.2025 | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 8 | 14 | 112 | | Arasınav için hazırlık | 10 | 2 | 20 | | Arasınav | 5 | 1 | 5 | | Ödev | 10 | 2 | 20 | | Dönem sonu sınavı için hazırlık | 10 | 1 | 10 | | Dönem sonu sınavı | 10 | 2 | 20 | | Total work load | | | 229 |
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