| Course Unit Title | Course Unit Code | Type of Course Unit | Level of Course Unit | Year of Study | Semester | ECTS Credits |
|---|---|---|---|---|---|---|
| Numerical Methods | MUH203 | Elective | Bachelor's degree | 2 | Fall | 3 |
Name of Lecturer(s)
Prof. Dr. Zahir MURADOĞLU
Prof. Dr. Bülent ORUÇ
Prof. Dr. Halil YİĞİT
Associate Prof. Dr. Mine Aylin BAYRAK
Associate Prof. Dr. Arzu COŞKUN
Associate Prof. Dr. Ergin ULUTAŞ
Research Assistant Dr. İrem ÇAY
Learning Outcomes of the Course Unit
1) Define the errors in numerical computations such as absolute, relative, modelling, truncation and round-off errors
2) Fit the curves and solutions of nonlinear equations
3) Apply polinomial and exponential approximation for curve fitting with least squares method
4) Define the simple iteration and linear interpolation methods
5) Correlate the relation between numerical differentiation and differentiation with equally spaced and randomly spaced points
6) Calculate numerical integration
Program Competencies-Learning Outcomes Relation
| Program Competencies | ||||||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | ||
| Learning Outcomes | ||||||||||||
| 1 | No relation | No relation | No relation | Low | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 2 | No relation | No relation | No relation | No relation | No relation | No relation | Low | No relation | No relation | No relation | No relation | |
| 3 | Low | No relation | No relation | No relation | No relation | No relation | No relation | No relation | Low | No relation | No relation | |
| 4 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 5 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 6 | No relation | No relation | No relation | No relation | Low | No relation | No relation | No relation | No relation | No relation | No relation | |
Mode of Delivery
Face to Face
Prerequisites and Co-Requisites
None
Recommended Optional Programme Components
Mathematics I, Mathematics II, Computer Programming in Geophysics
Course Contents
This course covers;errors in numerical computations, curve fitting, solutions of nonlinear equations, bisection method, finite differences, interpolation, numerical differentiation, numerical integration and Fourier series.
Weekly Schedule
1) Introduction, Definition of Numerical analysis and concepts, Algorithms2) Errors in numerical computations. Absolute, relative error. Data error. Truncation error. Round-off error.
3) Curve fitting (Regression). Least squares. Linear, polinomial, exponential approximation. Systems convertible to linear systems.
4) Exercises on curve fitting.
5) Solutions of nonlinear equations. Simple iteration method. Linear interpolation methods.
6) Solution of nonlinear equation systems. Simple iteration method. Newton-Raphson, Regula-FAlsi method
7) Bisection method, Müller method, examples and exercises.
8) Midterm examination/Assessment
9) Finite differences, finite difference operators. Forward, backward and central, differences. Finite difference tables.
10) Interpolation.Linear interpolation Lagrange interpolation.
11) Numerical differentiation. Differentiation with equally spaced and randomly spaced points. Relations between differentiation and difference operators. Differentiation with Central difference operators.
12) Exercices on finite differences and interpolation.
13) Numerical integration.. Belirlenmemiş katsayılar yöntemiyle sayısal integrasyon, Lagrange enterpolasyon formülü ile sayısal integrasyon. Sonlu fark formülleri ile sayısal integrasyon.
14) Exercises on numerical integration
15) Fourier series
16) Final examination
Recommended or Required Reading
1- Mühendisler İçin Sayısal Yöntemler,Raymond Canale , Steven Chapra Çevirmen: Prof.Dr.Hasan Heperkan Yayınevi: Literatür Yayıncılık
Planned Learning Activities and Teaching Methods
1) Lecture
2) Case Study
3) Problem Solving
Assessment Methods and Criteria
Contribution of Semester Studies to Course Grade |
20% |
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Contribution of Final Examination to Course Grade |
80% |
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Total | 100% | |||||||||||
Language of Instruction
Turkish
Work Placement(s)
Not Required