## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Module MAT-02-13-M-1

## Module Identification

Module Number Module Name CP (Effort)
MAT-02-13-M-1 Mathematics for Computer Science Students: Analysis 5.0 CP (150 h)

## Basedata

CP, Effort 5.0 CP = 150 h 1 Sem. in WiSe/SuSe  Bachelor (General) [DE] German Schweitzer, Pascal, Prof. Dr. (PROF | DEPT: INF) Böhm, Janko, Dr. (WMA | DEPT: MAT) Kämmerer, Florentine, Dr. (WMA | DEPT: MAT) Kunte, Michael, Dr. (WMA | DEPT: MAT) [MAT-Service] Mathematics for other Departments [INF-82.79-SG] B.Sc. Computer Science [NORM] Active

## Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V+2U MAT-02-13-K-1
Mathematics for Computer Science Students: Analysis
P 56 h 94 h
U-Schein
ja PL1 5.0 WiSe/SuSe
• About [MAT-02-13-K-1]: Title: "Mathematics for Computer Science Students: Analysis"; Presence-Time: 56 h; Self-Study: 94 h
• About [MAT-02-13-K-1]: The study achievement "[U-Schein] proof of successful participation in the exercise classes (ungraded)" must be obtained.
• It is a prerequisite for the examination for PL1.

## Examination achievement PL1

• Form of examination: written exam (Klausur) (75-105 Min.)
• Examination Frequency: each semester
• Examination number: 80214 ("Mathematics for Computer Science Students: Analysis")

## Contents

• integer and rational numbers, countability,
• sequences, convergence, real numbers, decimal fractions, Cauchy sequences, convergence criteria, application: existence and calculation of square roots,
• Series, geometric series, convergence and divergence criteria, Cauchy product of series,
• Functions, continuity, application: nested intervals and existence of zeros, intermediate value theorem,
• power series, exponential function and functional equation, sine and cosine,
• differentiability, derivation rules, derivation of power series, Taylor series, extreme values, mean value theorem, rule of l'Hospital, application (e.g. Newton's method),
• Riemann integral, antiderivative and fundamental theorem of calculus, integration rules,
• inverse function, logarithm, general powers, derivative of the inverse function, application: runtime analysis of algorithms,
• outlook on ideas and concepts of multivariate analysis: limit values and continuity in several variables, curves in ℝn, partial derivatives, gradient and Hesse matrix, Taylor formula and local extrema, applications (e.g. geometric modelling).

## Competencies / intended learning achievements

Upon successful completion of this module, the students have achieved the following learning outcomes:
• The students know and understand the basic concepts, statements and methods of one-dimensional analysis, and know applications of them in computer science.
• Based on an outlook, they have developed a basic understanding of the generalization of these concepts to multivariate analysis.
• They are trained in analytical thinking and their capacity for abstraction has been promoted.
• Using a structure-oriented approach, they have learned to comprehend mathematical proofs and to independently prove or disprove mathematical statements in simple examples.
• By working on the given exercises, they have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture.
• In addition, their abilities to present and to work in a team were promoted.

## Literature

• O. Forster: Analysis 1, Analysis 2,
• H. Heuser: Lehrbuch der Analysis, Teil 1 und Teil 2,
• M. Barner, F. Flohr: Analysis I, Analysis II,
• K. Königsberger: Analysis 1, Analysis 2,
• B. Kreußler, G. Pfister: Mathematik für Informatiker: Algebra, Analysis, Diskrete Strukturen.

## Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de)

## Requirements for attendance of the module (informal)

Prior or parallel participation in the course [MAT-02-11-K-1] is assumed.

None

## References to Module / Module Number [MAT-02-13-M-1]

Course of Study Section Choice/Obligation
[INF-82.79-SG] B.Sc. Computer Science [Compulsory Modules] Theoretical Foundations [P] Compulsory