Kursinhalt:

Der Kurs gibt eine Einführung in die mathematische Modellierung mit partiellen Differentialgleichungen. Behandelt wird eine Auswahl aus den folgenden Themen:

  • Grundlegende Prinzipien der Kontinuumsmechanik und Thermodynamik
  • Symmetrien und Erhaltungssätze
  • Variationsprinzipien
  • Herleitung und Diskussion von Modellen aus der Hydrodynamik, Festkörpermechanik, Thermoelastizität, Geodynamik, Klimaforschung oder Quantenmechanik

Die Lehrveranstaltung kann an der FU Berlin als erster Teil eines zweisemestrigen BMS Basic Courses "Mathematical Modeling with PDEs" besucht werden. Der zweite Teil wird durch die Lehrveranstaltung 19215301 + 19215302 "Mathematische Modellierung in der Klimaforschung" im darauffolgenden Sommersemester abgedeckt. 

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Course contents:

The course gives an introduction to mathematical modeling with partial differential equations. It discusses a selection of the following topics:  

  • General principles of continuum mechanics and thermodynamics
  • Symmetries and conservation laws
  • Variational principles
  • Derivation and discussion of models from hydrodynamics, solid mechanics, thermoelasticity, geodynamics, climate research or quantum mechanics

This course can be attended as the first part of the BMS Basic Course "Mathematical Modeling with PDEs", which stretches over two semesters at FU Berlin. The second part will be covered in the subsequent summer term by the course 19215301 + 19215302 "Mathematical Modelling in Climate Research". 

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Literature:

  • Eck, Garcke, Knabner - Mathematical Modeling
  • Temam, Miranville - Mathematical Modeling in Continuum Mechanics
  • Gurtin - An Introduction to Continuum Mechanics
  • Ciarlet - Mathematical Elasticity - Vol. I

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Lectures & Tutorials:

The course takes place weekly on the following dates:

  • Lecture: Fridays Thursdays, Tuesdays, 10:10 -- 11:50, A3/SR 115
    • does not take place on Nov 15, Nov 29, Dec 6, Dec 20
  • Tutorial: Tuesdays, 14:10 -- 15:50, A6/SR 009                                      
    • does not take place on Oct 29, Nov 12, Dec 3

Lecturer: Thomas Eiter (thomas.eiter@fu-berlin.de)
Office: Arnimallee 9, Room K012
Office hours: Fridays, 13:00 -- 14:00

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Completion requirements:

For successful completion of the course, the following requirements have to be met:

  1. regular participation in the tutorials:
    • attendance in at least 75 % of the tutorials
  2. active participation in the tutorials:
    • presentation of the solution to at least one (non-submitted) exercise on the blackboard
    • achievement of at least 50 % of the total homework points
      • the first exercise on each sheet can be submitted and will be graded
  3. successful completion of the final exam:
    • passing the oral exam, duration: about 20 minutes
      • individual dates will be arranged in due time