BIWO-04 Numerical Methods

lecturer

Prof. Dr.-Ing. habil. Reuter

contents and qualifications

content of the module: engineering design and analysis of algorithms for the numerical solution of continuous mathematical problems, direct methods that give the exact solution to a problem in a finite number of steps and for an infinite computer accuracy, iterative methods to compute approximations that converge to the exact solution of a problem, linear algebra and analytical geometry, solutions for linear and nonlinear equations, equation systems, extremum and eigenvalue problems, numerical integration, interpolation, regression and implementation of the algorithms in software solutions. On completion of the module students are able to apply basic and advanced numerical methods to solve engineering and scientific issues of civil engineering. Students will have the necessary programming knowledge to implement the numerical methods.

types of teaching and learning

2 SWS^* lecture and 2 SWS tutorial and also self-study

^*SWS = contact hours per week per semester

usability

The module is a required module in Master’s programme Advanced Computational and Civil Engineering Structural Studies (ACCESS). It is a prerequisite for the required elective module BIWE-12.

requirements for being awarded credits

Students can earn credit points after having passed the module exam. The module exam consists of a written exam (90 minutes) and an ungraded assigned paper with a total of 30 hours.

credits and grades

Students can earn 4 credit points through the module. The module grade is equivalent to the grade earned for the written exam if the assigned paper rated "pass". Otherwise, the module grade is the weighted average of the grade for the written exam and grade 5 for the assigned paper (§ 10 par. 1 sentence 5 PO); the weighting factors applied to the written exam and the assigned paper are two and one, respectively.

availability of the module

The module is offered in the winter semester.

workload

total workload 120 hours

duration of the module

1 semester

course materials

This information is made available in OPAL .

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

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