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401-0251-00L 6 Credits BSC D-HEST , D-ERDW , D-USYS
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Mathematics I

Mathematik I: Analysis I

Lecturers & Examiners: Peter Thurnheer
VVZ CR n/a

Last Updated: 2026-02-05 15:24:26

Abstract

This course treats the modelling, solving and discussion of concrete scientific problems - particularly by using differential equations. All the necessary mathematical aids for this topic, as well as concepts and questions of relevance to this process are gone into. An introduction into a computer algebra system (Maple) is integrated into the course.

Objective

Mathematics is of ever increasing importance to the Natural Sciences and Engineering. The key is the so-called mathematical modelling cycle, i.e. the translation of problems from outside of mathematics into mathematics, the study of the mathematical problems (often with the help of high level mathematical software packages) and the interpretation of the results in the original environment. The goal of Mathematics I is to get used to this paradigm with the help of relatively elementary examples. The indispensable prerequisite is facility with the basic notions from Calculus, i.e. functions and the notion of derivative. A very important tool of modelling is differential equations. They are therefore in the focus of both Mathematics I and Mathematics II (Part Linear Algebra).

Content

What is a differential equation? Modelling with differential equations. Differential equations from a geometrical and computational view point. Equilibria and their stability. Further topics: Least squares, Taylor polynomials and Taylor series, complex numbers.

Resources

Lecture Notes

Handouts zu verschiedenen Abschnitten

Literature

- H. H. Storrer: Einführung in die mathematische Behandlung der Naturwissenschaften, Birkhäuser Skripten

General Information

Language
German
Levels
BSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
oral 30 minutes

Course Components

Type Title Time & Place Hours
lecture Mathematik I: Analysis I
  • Mon 08:15-10:00 (HG E 7)
  • Thu 08:15-10:00 (HG E 7)
4 h weekly
exercise Mathematik I: Analysis I
Montag 15-17 bzw. Donnerstag 15-17 für Studiengang Umweltnaturwissenschaften. Mittwoch 13-15 für Studiengänge Agrarwissenschaft bzw. Erdwissenschaften bzw. Lebensmittelwissenschaft.
  • Mon 15:15-17:00 (HG E 33.3)
  • Mon 15:15-17:00 (HG F 26.3)
  • Mon 15:15-17:00 (HG F 26.5)
  • Wed 13:15-15:00 (ETZ F 91)
  • Wed 13:15-15:00 (ETZ H 91)
  • Wed 13:15-15:00 (HG E 5)
  • Wed 13:15-15:00 (HG F 26.1)
  • Wed 13:15-15:00 (HG F 26.5)
  • Wed 13:15-15:00 (HG G 26.5)
  • Wed 13:15-15:00 (LEO A 2)
  • Wed 13:15-15:00 (LFW E 13)
  • Thu 15:15-17:00 (HG G 3)
2 h weekly

Offered In