# 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): 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 the degree program B.Sc. Computer Science. Origin 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

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

Students

• Know basic calculus,
• understand the concept of limits in sequences, series, functions and power series,
• can recognize cross connections to their own discipline,
• can apply mathematical and, in particular, analytical ways of thinking and working to concrete problems, including technically motivated problems,
• have a mathematical intuition that can be translated into precise concepts and formal reasoning,
• have a trained ability to abstract,
• can discuss content from calculus in a structured manner in a group.

## Prerequisites

None. The competences taught in the following module are recommended: Basic Linear Algebra.

## Applicability

The module can be attended at FB12 in study program(s)

• B.Sc. Data Science
• B.Sc. Computer Science
• B.Sc. Business Informatics
• LAaG Computer Science
• BA Minor Mathematics
• BA Minor Computer Science

When studying B.Sc. Computer Science, this module must be completed in the study area Basic and Continuing Modules in Mathematics.

The module can also be used in other study programs (export module).

• 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