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| YZM3007 | Numerical Analysis | 2+2+0 | ECTS:5 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of SOFTWARE ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 2 hours of lectures and 2 hours of practicals per week | | Lecturer | Doç. Dr. Esma ULUTAŞ | | Co-Lecturer | | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | To give fundamental methods of numerical analysis. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | Understand about the errors resulting from the making of approximations while applying various numerical methods, and the ways to minimizing of these errors. | 1,2 | 1, | | LO - 2 : |
Understand about the weak and powerful sides, and skills of numerical methods and the computers. | 1,2 | 1, | | LO - 3 : | Choose the appropriate numerical method depend on the problem to be | 1,2 | 1, | | LO - 4 : | Obtain the basic numerical solution of ordinary differential equations. | 1,2 | 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 | | |
| Mathematical modeling concept, approximations and errors. Roots of equations. Systems of algebraic equations. Curve fitting. Interpolations. Tables of Finite Differences.Numerical differentiation and numerical integration. Solution of ODE's. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Motivation. Numerical methods and engineering practice. Mathematical modeling concept. | | | Week 2 |
Taylor series. Approximations and error definitions. Numerical errors; relative, absolute, approximation, truncation and truncation errors. | | | Week 3 |
Roots of equations. Barcketing methods: Bisection and false-position methods. | | | Week 4 | Open methods: Simple iteration, Newton-Raphson and Secant methods. Multiple roots. Comparison of various methods. | | | Week 5 | Lineer cebirsel denklemler. Küçük denklem sistemlerinin çözümü: Grafik yöntemler, Cramer kuralı ve bilinmeyenlerin yok edilmesi. | | | Week 6 |
Gauss elimination, Gauss-Jordan, Matrix inverse methods. Gauss-Saidel method. Weak and powerful sides of solution methods.
| | | Week 7 | Table of Finite Differences. Forward finite differences, backward finite differences and central differences. | | | Week 8 | Interpolation. Linear and higher order interpolations with Newton and Lagrange interpolating polynomials. | | | Week 9 | Mid-term Exam | | | Week 10 |
Numerical differentiation. Forward, backward and central approximations of differentiations. High order differentiation formulas. | | | Week 11 |
Numerical integration. Newton-Cotes integration formulas. Trapezoid rule. 1/3 ve 3/8 Simpson rules. | | | Week 12 | Numerical integration. Newton-Cotes integration formulas. Trapezoid rule. 1/3 ve 3/8 Simpson rules. | | | Week 13 | Ordinary differential equations and engineering practice | | | Week 14 | Numerical solutions of ordinary differential equations. Euler's and Runge-Kutta methods | | | Week 15 |
Multistep methods; Adams, Newton-cotes, Milne methods. | | | Week 16 | End-of-term exam | | | |
| 1 | Atkinson, K. 1989 An introduction to Numerical Analysis, John Wiley Pub. | | | |
| 1 | Bayram, Mustafa 2002; Nümerik Analiz, Aktif Yayınevi, Ankara. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 29.11.2023 | 2 | 50 | | End-of-term exam | 16 | 15.01.2024 | 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 | 4 | 14 | 56 | | Sınıf dışı çalışma | 4 | 14 | 56 | | Laboratuar çalışması | 0 | 0 | 0 | | Arasınav için hazırlık | 5 | 2 | 10 | | Arasınav | 2 | 1 | 2 | | Uygulama | 0 | 0 | 0 | | Klinik Uygulama | 0 | 0 | 0 | | Ödev | 0 | 0 | 0 | | Proje | 0 | 0 | 0 | | Kısa sınav | 0 | 0 | 0 | | Dönem sonu sınavı için hazırlık | 12 | 2 | 24 | | Dönem sonu sınavı | 2 | 1 | 2 | | Diğer 1 | 0 | 0 | 0 | | Diğer 2 | 0 | 0 | 0 | | Total work load | | | 150 |
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