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| MAT3002 | Numerical Analysis II | 4+0+0 | ECTS:6 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Dr. Öğr. Üyesi Muhammet YAZICI | | Co-Lecturer | Dr. Lecturer Muhammet YAZICI | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The aim of the course is to provide students the knowledge of numerical methods to handle problems with no analitical solutions or with solutions that are not practical to be used. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | learn about iterative methods for determinig zeros of a single variable function or solution of nonlinear algebraic systems and implement such methods in MATLAB/Octave environment. | 5,6 | 1 | | LO - 2 : | learn about direct and iterative methods for linear algebraic systems and implement such methods in MATLAB/Octave environment. | 5,6 | 1 | | LO - 3 : | learn about basic methods of numerical integration and implement such methods in MATLAB/Octave environment. | 5,6 | 1 | | 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), LO : Learning Outcome | | |
| Fixed point iteration method, Selection of a proper iteration function and the method of Newton-Raphson, Several variants of Newton-Raphson method, Newton methods and its variants for nonlinear algebraic ssytems, Linear algebraic ssytems and their solutions, Direct methods:Gauss elimination with no pivoting or partial pivoting, LU decomposition and solution by LU decomposition, Gram-Schmidt method of ortogonalization, QR decomposition with Gram-Schmidt method, solution by QR method, Least Square Method vs QR method, Iterative methods: Gauss-Jacobi, Gauss-Seidel and convergence of iterative methods. Numerical methods of integration(left and right rectangle, mid-point, trapezoidal, Simpson) and their composite forms, local and global errors, applications in MATLAB/Octave environment, Iterative methods(Romberg). |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Fixed point iteration method | | | Week 2 | Selection of iteration function and newton_Raphson method | | | Week 3 | Variants of Newton's method | | | Week 4 | Newton's method for nonlinear algebraic systems | | | Week 5 | Linear algebraic systems(overview) | | | Week 6 | Direct methods for Linear algebraic systems(Gauss elimination) | | | Week 7 | LU decomposition and solution by decomposition | | | Week 8 | QR decomposition and solution by QR decomposition | | | Week 9 | Midterm | | | Week 10 | İterative methods for linear systems(Gauss-Jacobi, Gauss-Seidel) | | | Week 11 | Convergence of iterative methods and applications in MATLAB/Octave | | | Week 12 | Numerical Integrations(simple methods) | | | Week 13 | Numerical integration(Composite Methods) | | | Week 14 | Applications in MATLAB/Octave | | | Week 15 | Error analysis in integration methods | | | Week 16 | Final exam | | | |
| 1 | Coşkun, Erhan; Sayısal Analize Giriş(MATLAB/Octave ile vektör cebirsel yaklaşım), KTÜ Basımevi, 2023. | | | 2 | Mathews, John H., Fink, Kurtis D. 1999; Numerical Methods using MATLAB, Prentice Hall, USA. | | | |
| 1 | Kincaid, D. , Cheney, W., 1991; Numerical Analysis Mathematics of Scientific Computing, Brooks/Cole, USA. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | | 01,30 | 30 | | In-term studies (second mid-term exam) | 4,7,12,14 | | | 20 | | End-of-term exam | 16 | | 1,30 | 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 | 4 | 14 | 56 | | Sınıf dışı çalışma | 5 | 14 | 70 | | Arasınav için hazırlık | 10 | 1 | 10 | | Arasınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 10 | 1 | 10 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 150 |
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