BIWO-04 Numerical Methods

module description according study regulations for the consecutive Master's degree program ACCESS as of 17th August 2022

Course materials are available in OPAL .

detail contents of "Numerical Methods":

Introduction to Numerical Analysis

• types and stability of algorithm
• condition of problems

Programming with Fortran 90/95

• structur of program
• basic elements
• declaration of variables
• arithmetic and logical operators
• conditional statements and loops
• input and output

Linear algebra

• vector calculus, matrix calculus
• aystems of linear equations
• apecific eigenvalue problem
• generalized eigenvalue problem

Systems of non-linear equations

• Bisection method, secant method, regula falsi method
• Newton’s method

Extremum problems

Numerical integration

• Quadrature rules based on interpolating functions
• Monte Carlo integration (simulation)

Approximation

• function approximation
• approximation of discrete data
• polynomial interpolation vs. spline interpolation
• interpolation vs. regression analysis

Computer graphics

• coordinate transformation
• projection

recommended literature:

R.Kress: Numercial Analysis, Spinger, New York Berlin Heidelberg, 1998

D.V.Griffiths, I.M.Smith: Numerical methods for engineers - a progamming approach, Blackwell Scientific, London, 1991