Introduction to Mathematical Modeling (ILS-MA-M3)10.0 ECTS
(englische Bezeichnung: Introduction to Mathematical Modeling)

Lehrveranstaltungen:

• • Mathematische Modellierung Theorie
    (Vorlesung, 2 SWS, Serge Kräutle)
  • Übungen zur Mathematische Modellierung Theorie
    (Übung, 2 SWS, Nadja Ray et al.)
  • Mathematische Modellierung Praxis
    (Praktikum, 2 SWS, Martin Burger)

Empfohlene Voraussetzungen:

Modules of analysis and linear algebra or introductory math courses of two semesters are strongly recommended. Basic Knowledge in numerical mathematics (use of MATLAB) and knowledge in ordinary differential equations is recommended.

Inhalt:

The module combines theory and practice, it links and extends the contents of various introductory math courses. Theory: (lecture and tutorial)

• Methods (basic tools) of mathematical modeling, such as dimensional analysis, asymptotic expansions, stability, sensitivity, existence and positivity of solutions

• Models given by linear systems (electric circuits, girder bridge, relation to minimization problems), by non‐linear systems of equations (chemical reactions), and by initial value problems of differential equations (predator‐prey models, biological models) Practice: (project work in team): Modeling, analytical investigation and solving of problems coming from engineering and natural sciences (e.g. mechanics or life science).

Lernziele und Kompetenzen:

The students

• get to know the basic methods of mathematical modelling and apply the approaches to real‐life problems

• develop, analyse and evaluate mathematical models given by systems of algebraic or differential equations

• solve real‐life problems in a team by using analytical and numerical methods

• develop the competence to solve general problems

• develop management skills (team work, time and project management), are empowered by reporting in the projects to lecture presentation and scientific writing (The attendance of the project is compulsory due to the teamwork.)

Literatur:

• Ch. Eck, H. Garcke, P. Knabner. "Mathematische Modellierung". Springer-Verlag, 2. Auflage, Berlin 2011

• F. Hauser, Y. Luchko. "Mathematische Modellierung mit MATLAB“. Spektrum Akademischer Verlag 2011

• G. Strang. "Introduction to Applied Mathematics". Wellesley‐Cambridge Press, Wellesley 1986

Verwendbarkeit des Moduls / Einpassung in den Musterstudienplan:
Das Modul ist im Kontext der folgenden Studienfächer/Vertiefungsrichtungen verwendbar:

1. Integrated Life Sciences: Biology, Biomathematics, Biophysics (Master of Science)
   (Po-Vers. 2015w | NatFak | Integrated Life Sciences: Biology, Biomathematics, Biophysics (Master of Science) | Module Groups | MG1: Mathematical Modelling and Systems Biology | Mandatory Elective Modules Group 1 | Introduction to Mathematical Modeling)
2. Integrated Life Sciences: Biology, Biomathematics, Biophysics (Master of Science)
   (Po-Vers. 2019w | NatFak | Integrated Life Sciences: Biology, Biomathematics, Biophysics (Master of Science) | Module Groups | MG1: Mathematical Modelling and Systems Biology | Mandatory Elective Modules Group 1 | Introduction to Mathematical Modeling)

Studien-/Prüfungsleistungen:

Introduction to Mathematical Modeling (Prüfungsnummer: 81611)

(englischer Titel: Introduction to Mathematical Modeling)

Prüfungsleistung, mehrteilige Prüfung, Dauer (in Minuten): 15, benotet, 10.0 ECTS

Anteil an der Berechnung der Modulnote: 100.0 %

weitere Erläuterungen:
Theorie: muendliche Pruefung 15 Min, Uebungen, Praxis:muendliche Praesentation 15 min, Bericht

Prüfungssprache: Deutsch oder Englisch

Erstablegung: WS 2020/2021, 1. Wdh.: WS 2020/2021

1. Prüfer:

Serge Kräutle