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| MAT3029 | Numerical Analysis I | 4+0+0 | ECTS:6 | | Year / Semester | Fall 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 | Prof. Dr. Erhan COŞKUN | | Co-Lecturer | | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The purpose of the course is to develop skills to numerically analyze elementary problems using MATLAB/OCTAVE as an analysis tool. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | Develop codes for elementary problems in numerical analysis using MATLAB/OCTAVE | 3,4,5,6 | 1, | | LO - 2 : | numerically analyze elementary problems | 3,4,5,6 | 1, | | LO - 3 : | have knowledge on numerical methods for elementary problems | 3,4,5,6 | 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 | | |
| The need for numerical analysis, the stages of numerical analysis, coding with MATLAB/OCTAVE (conditional structures, loops and function programs, review). Finding an interval containing a zero of a function, the principles of numercial analysis using a paradigm problem of approximating a real zero of a function. Computer number system. Representation of real numbers in computers and related errors. Approximation of a function around a point using Taylor polynomials and resulting errors. Estimating an unknown value in a data set using polynomials and resultant errors (algebraic formulation, Lagrange, Newton and spline interpolations). Approximating a function over an interval using elemantary functions and related error.
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | The need for numerical analysis and its stages, error types. | | | Week 2 | Recall: algorithm design, coding with OCTAVE/MATLAB | | | Week 3 | Numerical analysis process with finding zeros of a function | | | Week 4 | Computer number system and change of basis. | | | Week 5 | Errors related to computer number system | | | Week 6 | Approximating a function about a point using polynomials | | | Week 7 | Errors in polynomials aproximation and Horner's methods. | | | Week 8 | Interpolation with a set of ordered pairs in R^2 (Algebraic, Newton and Lagrange formulations) | | | Week 9 | Midterm | | | Week 10 | Lagrange formulation | | | Week 11 | Error in interpolation | | | Week 12 | Coding of interpolation problems with OCTAVE/MATLAB, spline interpolation | | | Week 13 | Aproximating a data set via elementary functions | | | Week 14 | Aproximating a function defined over an interval via elementary functions | | | Week 15 | Review | | | Week 16 | Final exam | | | |
| 1 | Coşkun, E. Sayısal Analize Giriş(MATLAB/Octave ile vektör cebirsel yaklaşım) , KTÜ Basımevi, 2223 | | | |
| 1 | Mathews, J.H., Fink, K.D. 1999; Numerical Methods Using MATLAB, Prentice Hall. | | | 2 | Burden, R.L., Faires, J.D. 2011; Numerical Analysis, Brooks/Cole Cengage Learning, Toronto. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 26/11/2023 | 2 saat | 30 | | In-term studies (second mid-term exam) | 4,7,12,14 | | 15dk | 20 | | End-of-term exam | 16 | 16/01/2024 | 2 saat | 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 | 4 | 14 | 56 | | Arasınav için hazırlık | 15 | 1 | 15 | | Arasınav | 2 | 1 | 2 | | Kısa sınav | 6 | 4 | 24 | | Dönem sonu sınavı için hazırlık | 20 | 1 | 20 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 175 |
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