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German original

Basics of Advanced Mathematics
(dt. Grundlagen der Höheren Mathematik)

Level, degree of commitment in original study programme Intermediate module, required module
Forms of teaching and learning,
workload		 Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements		 9 CP
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
Language,
Grading		 German,
The grading is done with 0 to 15 points according to the examination regulations for study course B.Sc. Data Science.
Original study programme B.Sc. Data Science / Mathematik Aufbaumodule
Duration,
frequency		 One semester,
each winter semester
Person in charge of the module's outline Prof. Dr. Ilka Agricola

Contents

  • Deepening of linear algebra: Jordan normal form, diagonalization of matrices, principal axes theorem, quadrics
  • Multidimensional differential calculus: directional derivation, partial and total derivation, gradient, Hesse's form, extremes with and without constraints
  • Multidimensional integral calculus: Volume, multiple integrals, main theorem of integral calculus

Qualification Goals

The students shall

  • learn analytical and algebraic methods to solve problems of higher mathematics, especially numerics and optimization,
  • practice the handling of functions in several variables (differential and integral calculus in several variables),
  • improve their oral communication skills in the exercises by practicing free speech in front of an audience and during discussion.

Prerequisites

None. The competences taught in the following modules are recommended: Basic Linear Algebra, Basic Real Analysis.


Recommended Reading

  • K. Meyberg, P. Vachenauer, Höhere Mathematik, Band 1 und 2, Springer-Verlag.
  • G. Teschl, S. Teschl: Mathematik für Informatiker, Band 1 und 2, Springer-Verlag.



Please note:

This page describes a module according to the latest valid module guide in Wintersemester 2022/23. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.