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Mühendislik Mimarlık Fakültesi - Bolumderslericerik Muhendislik
Course unit title Level of course unit Course unit code Type of course unit L+R C ECTS
Numerical Methods BIM-210 Compulsory 4 25 4

Description of course unit

Prerequisites and course requisities -
Language of instruction Turkish
Teaching assitant(s)
Mode of delivery Face to face
Course objective This course is designed to introduce engineering students to the numerical solutions of mathematical problems occurring in engineering and to improve their computer skills.
Course description Matrix operations, solving of linear and nonlinear algebraic equations,linear interpolation, numerical integration and differentiation and numerical solution of ordinary differential equations are explained

Course contents

1- Matrix Operations
2- Solution of the systems of linear equations, Direct methods: Gaussian elimination, Gauss Jordan elimination
3- Iterative methods for linear systems, simple iteration, Gauss-Seidel , relaxation
4- Numerical solution of nonlinear equations, Bisection Method, Linear İnterpolation - Regula Falsi Method
5- Simple iteration, Newton-Raphson, Sekant methods
6- Nonlinear equation systems and solutions
7- Curve fitting and interpolation, intepolation polynomials, linear interpolation,Lagrange Polynomials, Neville Methods
8- Divided differences, cubic spline curves, partial cubic spline curves, least square method
9- Numerical differentiation, Forward, backward, and central differance differentiation formulas
10- Numerical Integration, Trapez Rule, Romberg Integration, Simpson Rule
11- Gauss kuadratur, multi variable integration
12- Solution of Ordinary Differential Equations, Euler Method, improved Euler method
13- Initial value problem
14- Boundary value problems

Learning outcomes of the course unit

1- Be familiar with matrix operations
2- Be able to use numerical methods to solve linear and nonlinear algebraic equations
3- Ability to interpolate any data
4- Ability to differentiate and integrate any data, numerically
5- Ability to solve numerically ordinary differential equations
6- Ability to explain the advantages and disadvantages of alternative numerical methods
7- Be able to make the computer implementation of these numerical methods to solve fundamental and practical engineering problems and to develop programming skills
8- Ability to recognize the importance of errors and be able to estimate the errors in numerical solution