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| ME3003 | Numerical Analysis | 3+0+0 | ECTS:4 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of MECHANICAL ENGINEERING | | Prerequisites and co-requisites | DC must have been achieved from ME1002-Computer Programming or DC must have been achieved from ME1000-Computer Programming | | Mode of Delivery | | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Doç. Dr. Mert GÜLÜM | | Co-Lecturer | Doç. Dr. Mert GÜLÜM | | Language of instruction | | | Professional practise ( internship ) | None | | | | The aim of the course: | | To give fundamental methods of numerical analysis. To apply these methods by using a high-level technical programming language, such as MATLAB. To improve the student's computer skills. |
| 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 solved. | 1,2 | 1 | | LO - 4 : | apply the basic numerical solution techniques by using a high-level programming language, such as MATLAB. | 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. Numerical differentiation and numerical integration. Solution of ODE's. Application of the numerical methods using MATLAB programming language. |
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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. Sources of numerical errors. | | | Week 3 | Numerical differentiation. Forward, backward and central approximations of differentiations. High order differentiation formulas. | | | Week 4 | Roots of equations. Barcketing methods: Bisection and false-position methods. | | | Week 5 | Open methods: Simple iteration, Newton-Raphson and Secant methods. Multiple roots. Comparison of various methods. | | | Week 6 | Linear algebraic equations. Solution methods for small numbers of equations: Graphical methods, Cramer's rule and elimination of unknows. | | | Week 7 | Gauss elimination, Gauss-Jordan, Matrix inverse methods. Gauss-Saidel method. Weak and powerful sides of solution methods. | | | Week 8 | Curve fitting and engineering practice. Least-square regression. Linear regression. Linearization of non-linear relationships. Polinomial regression. | | | Week 9 | Mid-term Exam | | | Week 10 | Interpolation. Linear and higher order interpolations with Newton and Lagrange interpolating polynomials. | | | Week 11 | Numerical integration. Newton-Cotes integration formulas. Trapezoidal rule. 1/3 and 3/8 Simpson rules. | | | Week 12 | Numerical integration. Newton-Cotes integration formulas. Trapezoidal rule. 1/3 and 3/8 Simpson rules. | | | Week 13 | Ordinary differential equations and engineering practice. Euler's method. | | | Week 14 | Heun's and Runge-Kutta methods. Numerical sollutions of ordinary differential equation systems. | | | Week 15 | Numerical sollutions of ordinary differential equation systems. | | | Week 16 | End-of-term exam | | | |
| 1 | Chapra, Steven C., Canale Raymond P. 1998; Numerical methods for engineers: with programming and software, 3rd ed., McGraw-Hill, New York. | | | 2 | Heperkan, H., Kesgin, U., 2003; Yazilim ve programlama uygulamalariyla mühendisler için sayisal yöntemler ("Numerical methods for engineers: with programming and software" kitabinin 4. basiminin çevirisi), Literatür yayincilik, Istanbul. | | | |
| 1 | Mathews, John H., Fink, Kurtis D., 1999; Numerical methodsusing MATLAB, Prentice Hall, New York. | | | 2 | Fausett, Laurene V., 1999; Applied numerical analysis using MATLAB, Prentice Hall, New York. | | | 3 | Herniter, Marc E., 2001; Programming in MATLAB, Thomson Learning, Australia. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 30/11/2023 | 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 | 3 | 14 | 42 | | Sınıf dışı çalışma | 3 | 10 | 30 | | Arasınav için hazırlık | 2 | 8 | 16 | | Arasınav | 2 | 1 | 2 | | Uygulama | 1 | 5 | 5 | | Ödev | 3 | 4 | 12 | | Kısa sınav | 1 | 1 | 1 | | Dönem sonu sınavı için hazırlık | 2 | 5 | 10 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 120 |
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