## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Course MAT-02-13-K-1

## Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 5.0 CP 94 h
2 V Lecture 28 h
2 U Exercise class (in small groups) 28 h
(2V+2U) 5.0 CP 56 h 94 h

## Basedata

SWS 2V+2U 5.0 CP = 150 h 1 Sem. in WiSe/SuSe  Bachelor (General) [DE] German Böhm, Janko, Dr. (WMA | DEPT: MAT) Kämmerer, Florentine, Dr. (WMA | DEPT: MAT) Kunte, Michael, Dr. (WMA | DEPT: MAT) [MAT-Service] Mathematics for other Departments [NORM] Active

## Possible Study achievement

• Verification of study performance: proof of successful participation in the exercise classes (ungraded)
• Details of the examination (type, duration, criteria) will be announced at the beginning of the course.

## 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).

## 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.

## Materials

Further literature will be announced in the lecture(s); exercise material is provided.

## Registration

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

## Requirements for attendance (informal)

A previous or parallel participation in the course [MAT-02-11-K-1] "Mathematics for Computer Science Students: Algebraic Structures" is assumed.

None

## References to Course [MAT-02-13-K-1]

Module Name Context
[MAT-02-13-M-1] Mathematics for Computer Science Students: Analysis P: Obligatory 2V+2U, 5.0 LP