Course Applied Statistics and Numerical Analysis

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Responsible: Prof.Dr. Schellong

Course

Meets requirements of following modules(MID)

• in active programs
  • Ba ET2012 AM
  • Ba TIN2012 AM

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): 120-150

Instruction language

• German

Study Level

• Undergraduate

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

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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

Aquired 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