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German original

Basic Real Analysis
(dt. Grundlagen der Analysis)

Level, degree of commitment in original study programme Basic 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 examination
Language,
Grading
German,
The grading is done with 0 to 15 points according to the examination regulations for study course B.Sc. Computer Sciences.
Original study programme B.Sc. Informatik / Mathematik Pflichtmodule
Duration,
frequency
One semester,
each summer semester
Person in charge of the module's outline Prof. Dr. Hajo Holzmann, Dr. Dorothea Strauer

Contents

Basics of the mathematical language

  • Basics of logic and sets
  • Proof methods, mathematical induction
  • Real numbers, functions, inequations
  • Countability
  • Factorials, binomial coefficients, binomial theorem

Sequences and series

  • Properties of sequences and series, limits
  • Convergence criteria
  • Landau symbols

Functions of one variable

  • Exponential function and trigonometric functions
  • Limit values, continuity, monotony
  • Intermediate value theorem, theorem of minimum and maximum
  • Power series

Differentiability

  • Affine-linear approximation
  • Derivation rules
  • Mean value theorem of differential calculus
  • Local extrema
  • Taylor expansion

Integrability

  • Main theorem of differential and integral calculus,
  • Integration rules
  • Improper integrals

Qualification Goals

The students shall

  • acquire basic knowledge and skills in analysis, in particular an understanding of the concept of limit values for sequences, series, functions and power series,
  • Recognize connections to their own discipline,
  • practice mathematical and in particular analytical ways of thinking and working on concrete questions, also on technically motivated problems,
  • develop mathematical intuition and learn how to translate it into precise terms and formal justifications,
  • to train their abstraction skills,
  • 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 module are recommended: Basic Linear Algebra.


Recommended Reading

  • Dörfler, W.; Peschek, W. : Einführung in die Mathematik für Informatiker, Hanser
  • Wolff, M.; Gloor, O.; Richard, Chr. : Analysis Alive, Birkhäuser
  • Forster, O. : Analysis 1, Vieweg
  • Hachenberger, D.: Mathematik für Informatiker, Pearson
  • Oberguggenberger, M.; Ostermann, A.: Analysis for Computer Scientists, Springer
  • Teschl, G.; Teschl, S.: Mathematik für Informatiker, Band 2: Analysis und Statistik, Springer



Please note:

This page describes a module according to the latest valid module guide in Wintersemester 2020/21. 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.