Course Applied Statistics and Numerical Analysis


Responsible: Prof.Dr. Schellong

Course

Meets requirements of following modules(MID)

Course Organization

Version
created 2012-06-29
VID 1
valid from WS 2012/13
valid to
Course identifiers
Long name Applied Statistics and Numerical Analysis
CID F07_ASN
CEID (exam identifier)

Contact hours per week (SWS)
Lecture 2
Exercise (unsplit)
Exercise (split)
Lab 1
Project
Seminar
Tutorial(voluntary) 2
Total contact hours
Lecture 30
Exercise (unsplit)
Exercise (split)
Lab 15
Project
Seminar
Tutorial (voluntary) 30
Max. capacity
Exercise (unsplit)
Exercise (split) 40
Lab 18
Project
Seminar

Total effort (hours): 150

Instruction language

  • German

Study Level

  • Bachelor

Prerequisites

  • Real functions of one and more variables
  • Differential and Integral Calculus
  • Linear Algebra (Matrices, Equation Systems)
  • basic skills in procedural programming

Textbooks, Recommended Reading

  • Knorrenschild: Numerische Mathematik (Fachbuchverlag)
  • Papula: Mathematik für Ingenieure und Naturwissenschaftler, Band 1+2 (Vieweg)
  • Preuß, Wenisch: Lehr- und Übungsbuch Numerische Mathematik (Fachbuchverlag)

Instructors

  • Prof.Dr. Schellong
  • Prof. Dr. Randerath

Supporting Scientific Staff

Transcipt Entry

Applied Statistics and Numerical Analysis

Assessment

Type
we written exam

Total effort [hours]
we written exam

Frequency: 2/year


Course components

Lecture/Exercise

Objectives

Contents
  • Mathematical modelling
    • system design
    • abstraction
    • structuring
    • algorithm
    • classes of mathematical models
  • Simulation
    • computer arithmetic
      • represenation of numbers
      • floating point arithmetic
      • error propagation and estimation
    • numerical solution of nonlinear equations
      • bisection
      • fix point procedure
      • Newton procedure
      • convergence order
    • numerical solution of linear equation systems
      • Gauß algorithm
      • LR-decomposition
      • iteration procedure
        • Jacobi
        • Gauß-Seidel
    • numerical solution of nonlinear equation systems
      • fix point procedure
      • Newton procedure
        • Jacobi-matrix
        • Simplified Newton procedure
        • damping procedure
    • approximations
      • interpolation
        • intepolation polynomial
        • spline-Interpolation
      • numerical integration
        • rectangular and trapez procedures
        • Simpson procedure
      • numerical solution of ordinary differential equations
        • Euler and modifications
        • Runge-Kutta-procedure
    • statistical basics
    • regression analysis
      • modelling
      • parameter estimation
      • statistical analysis
      • energy demand forecast
    • simulation tools

Acquired Skills
  • mathematical models
    • description of mathematical models
    • application of mathematical models to selected technical problems
  • numerical procedures
    • selection of appropriate algoritms
    • construction of algorithms
    • numerical simualtion using appropriate tools
    • evaluation of numerical results

Additional Component Assessment

Type
fPS exercise (on course and self study)

Contribution to course grade
fPS exercise (on course and self study)

Frequency: 1/year

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