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