|
Links
Ministery of Higher Education
Ministery of Higher Education in
Erbil
Salahaddin University
University of Sulaimani
Koya University
University
of Kurdistan
|
Numerical Analysis
Total hours:60 theory + 60 practice.
The aim of this subject is:
The purpose of numerical analysis is two-fold:
to find acceptable approximate solutions when exact solutions are either impossible or so arduous and time-consuming as to be impractical,
to devise alternate methods of solution better suited to the capabilities of computers.
Subjects Names:
- Numerical Analysis :
- Introduction(Definition of Numerical Analysis )
- some type of Errors
- Absolute Error
- Relative Error
- Rounding Error
- Solution of nonlinear Equations:
- Introduction
- bisection method
- False position method
- Secant method
- Newton- Raphson method
- Fixed point theorem.
- Steffensen's method
- Horner's method
- Solution of system nonlinear Equations:
- Newton –Raphson method ( for system)
- Fixed point method (for system)
- Direct Methods for solving linear system:
- Introduction to vectors and metrices
- Upper-triangular linear system
- Gaussian Elimination
- Triangular factorization.
- Iterative methods for solving linear system:
- Jacobi's method
- Gauss –Siedal method.
- Numerical interpolation and Extrapolation:
- Lagrange method
- Finite differences
- forward differences
- backward differences
- Newton differences
- Numerical Differentiation:
- Introduction
- Numerical Differentiation Formula
- Approximation the Derivative.
- Numerical integration :
- Introduction
- Composite Trapezoidal Rule
- Composite Simpson's Rule
- Romberg Integration
- Gauss Legendre integration
- Solution of Differential equation:
- Introduction
- Taylor methods
- Euler's method
- Modified Euler's method
- Heun's method
- Midpoint method
- Runge-Kutta Method of second order
- Runge-Kutta Method of fourth order
System of Differential Equations
********************************************************
References
Atkinson, L.V. and Harley, P.j.,"An Introduction to Numerical methods with Pascal". Addoson-wesely Publishing company, 1983.
Burden, B.l. and Faires, J.I. "Numerical Analysis", printed in United state of America, seventh edition 2001.
Conte, S.D. and Deboor, C. "Elementary Numerical analysis", McGraw-Hill Book Company, Newyork. Third edition, 1980.
Lambert, J.D., "Cmputational methods in ordinary Differential Equation", printed in Great Britain by J.w.Arrowsmith, Ltd, Bristol. 1981.
|
