151-0709-00L  Stochastic Methods for Engineers and Natural Scientists

SemesterAutumn Semester 2016
LecturersD. W. Meyer-Massetti, N. Noiray
Periodicityyearly recurring course
Language of instructionEnglish

AbstractThe course provides an introduction into stochastic methods that are applicable for example for the description and modeling of turbulent and subsurface flows. Moreover, mathematical techniques are presented that are used to quantify uncertainty in various engineering applications.
ObjectiveBy the end of the course you should be able to mathematically describe random quantities and their effect on physical systems. Moreover, you should be able to develop basic stochastic models of such systems.
Content- Probability theory, single and multiple random variables, mappings of random variables
- Stochastic differential equations, Ito calculus, PDF evolution equations
- Polynomial chaos and other expansion methods
All topics are illustrated with application examples from engineering.
Lecture notesDetailed lecture notes will be provided.
LiteratureSome textbooks related to the material covered in the course:
Stochastic Methods: A Handbook for the Natural and Social Sciences, Crispin Gardiner, Springer, 2010
The Fokker-Planck Equation: Methods of Solutions and Applications, Hannes Risken, Springer, 1996
Turbulent Flows, S.B. Pope, Cambridge University Press, 2000
Spectral Methods for Uncertainty Quantification, O.P. Le Maitre and O.M. Knio, Springer, 2010