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| GEM3000 | Numerical Methods | 2+0+0 | ECTS:2 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Elective | | Department | NAVAL ARCHITECTURE and MARINE ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 2 hours of lectures per week | | Lecturer | Doç. Dr. İsmail ALTIN | | Co-Lecturer | | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | Learning the fundamental numerical methods used in engineering. Giving the estimating methods of errors encountered in numerical calculations. Learning solution techniques for linear equations, linear interpolation, curve fitting, numerical differentiation and integration and numerical solution methods of differential equations. Giving an example problem concerning each solution technique. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | learn fundamentals of numerical analysis. | 4 | 1,3, | | LO - 2 : | compare different numerical methods recommended for a specified problem and can choose one of them to solve this problem. | 4 | 1,3, | | LO - 3 : | propose a mathematical model for a given engineering problem and can solve this problem with a suited numerical method. | 4 | 1,3, | | LO - 4 : | develop a computer program for numerical solution of a given engineering problem. | 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), LO : Learning Outcome | | |
| Errors. Numerical Solution of Linear equations. Finite differences. Taylor series. Linear interpolation. Curve fitting by means of least square method. Numerical differentiation. Numerical integration. Numerical solution methods for differential equations. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Errors. Solution of nonlinear equations:Simple iteration method. | | | Week 2 | Solution of nonlinear equations:Newton Raphson method, Secant method, Bisection method | | | Week 3 | Solution of systems of linear algebraic equations: Gauss elemination method, Gauss Jordan method. | | | Week 4 | Solution of systems of linear algebraic equations:Choleski method, Gauss Siedel method. | | | Week 5 | Solution of systems of linear algebraic equations: Jacopi method. | | | Week 6 | Solution of systems of nonlinear algebraic equations:Runge Kutta method. | | | Week 7 | Finite differences and Taylor series. | | | Week 8 | Interpolation: Gregory-Newton interpolation. | | | Week 9 | Mid-term exam | | | Week 10 | Interpolation:Lagrange interpolation. | | | Week 11 | Numerical differentiation. | | | Week 12 | Numerical integrasyon. | | | Week 13 | Numerical integrasyon. | | | Week 14 | Numerical solution methods for differential equations. | | | Week 15 | Curve fitting by means of least square method. | | | Week 16 | End-of-term exam | | | |
| 1 | Akpınar, S. 1994, Sayısal Çözümleme, KTÜ Müh. Mim. Fak. Fakülte Ders Notları, No: 39, Trabzon. | | | |
| 1 | Tapramaz, R. 2002, Sayısal Çözümleme, Literatür yayıncılık, İstanbul. | | | 2 | Chapra, C.S., Canale, R.P., Numerical Methods for Engineers, McGraw-hill Book Company, New York. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 17/04/2019 | 2 | 50 | | End-of-term exam | 16 | 07/06/2019 | 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 | 2 | 14 | 28 | | Sınıf dışı çalışma | 1 | 14 | 14 | | Arasınav için hazırlık | 3 | 1 | 3 | | Arasınav | 2 | 1 | 2 | | Ödev | 1 | 7 | 7 | | Dönem sonu sınavı için hazırlık | 4 | 1 | 4 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 60 |
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