This entry is from Winter semester 2018/19 and might be obsolete. You can find a current equivalent here.

# CS 280 — Basic Real Analysis (dt. Grundlagen der Analysis)

 Level, degree of commitment Basic module, depends on importing study program 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(s): Written examination Examination type: Successful completion of at least 50 percent of the points from the weekly exercises. Language,Grading German,The grading is done with 0 to 15 points according to the examination regulations for the degree program B.Sc. Computer Science. Subject, Origin Mathematics, B.Sc. Computer Science Duration,frequency One semester, each summer semester Person in charge of the module's outline Prof. Dr. Hajo Holzmann, Dr. Dorothea Strauer

## Contents

• Real numbers: Axioms and properties, completeness axiom and interval nesting, representation in computer,
• Sequences and series: properties, limits and inheritance rules, convergence criteria, Landau symbols,
• Functions: Limit values and continuity, intermediate value theorem, theorem of minimum and maximum, differentiability incl. affin-linear approximation, derivation rules, numerical differentiation, local extremes, integrability, integration rules, numerical integration, non-actual integrals, mean value theorems, main theorem of differential and integral calculus,
• Function sequences and series: point by point and uniform convergence, power series, Taylor development

## 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

Translation is missing. Here is the German original:

Keine. Empfohlen werden die Kompetenzen, die im Modul Grundlagen der Linearen Algebra vermittelt werden.

• 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