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

Courses

Catalogue data

Abstract	The 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.
Learning objective	By 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 - Estimation of statistical moments and probability densities based on data - Stochastic differential equations, Ito calculus, PDF evolution equations - Monte Carlo integration with importance and stratified sampling - Markov-chain Monte Carlo sampling - Control-variate and multi-level Monte Carlo estimation - Statistical tests for means and goodness-of-fit All topics are illustrated with engineering applications.
Lecture notes	Detailed lecture notes will be provided.
Literature	Some 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
Competencies	Subject-specific Competencies Concepts and Theories assessed Techniques and Technologies assessed Method-specific Competencies Analytical Competencies assessed Decision-making assessed Media and Digital Technologies assessed Problem-solving assessed Personal Competencies Creative Thinking assessed Critical Thinking assessed Integrity and Work Ethics assessed Self-direction and Self-management assessed

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits	4 credits
Examiners	D. W. Meyer-Massetti
Type	session examination
Language of examination	English
Repetition	The performance assessment is only offered in the session after the course unit. Repetition only possible after re-enrolling.
Mode of examination	written 60 minutes
Written aids	no aides are allowed
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

Groups

Restrictions

Offered in

Programme	Section	Type
Computer Science Bachelor	Minor Courses	W
Mechanical Engineering Master	Energy, Flows and Processes	W
Computational Science and Engineering Bachelor	Fluid Dynamics	W
Computational Science and Engineering Master	Fluid Dynamics	W