Universität Wien
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250160 VU Modelling interacting particle systems in Science (2019W)

7.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Continuous assessment of course work
Moodle

Details

max. 25 participants
Language: English

Lecturers

Classes (iCal) - next class is marked with N

No registration via u:space; For registration be present in the first unit;

  • Wednesday 02.10. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 03.10. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 09.10. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 10.10. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 16.10. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 17.10. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 23.10. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 24.10. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 30.10. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 31.10. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 06.11. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 07.11. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 13.11. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 14.11. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 20.11. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 21.11. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 27.11. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 28.11. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 04.12. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 05.12. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 11.12. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 12.12. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 08.01. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 09.01. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 15.01. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 16.01. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 22.01. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 23.01. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 29.01. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 30.01. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

The goal of this course is for students to learn how to model systems constituted by many particles. These systems can correspond, among many, to collective dynamics (flocking, pedestrian dynamics), opinion formation, cell dynamics, gas dynamics,...

Modelling requires knowledge from a wide variety of mathematical fields (particularly, probability and differential equations). This course will teach the basics needed. It will also show what constitutes a good mathematical model.

During the course the models presented in research papers will be read and analysed. By the end of the course, students should be able to understand the meaning of the models presented in these papers as well as being able to propose their own.

Topics covered include:
- modelling using Markov Chains, Markov Processes and Piece-wise Deterministic Markov Processes;
- modelling using Stochastic Differential Equations;
- modelling using Ordinary Differential Equations; Newton's law; minimisation of potential;
- computational models;
- derivation of partial differential equations (transport equations).

Assessment and permitted materials

This is a practical course, so attendance is compulsory, only a maximum of 5 classes can be missed. Evaluation will be based on exercises and quizzes carried out during the course plus a mid-term and final exam.

Minimum requirements and assessment criteria

The course is in English.
Good knowledge of mathematical analysis is required as well as basic knowledge in Probability (concepts like probability space, random variable, probability distribution).
Basic knowledge of ordinary differential equations.

Examination topics

Reading list

Association in the course directory

MFE

Last modified: Mo 07.09.2020 15:21