## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Course MAT-00-01-K-1

## Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 8.0 CP 156 h
4 V Lecture 56 h
2 U Exercise class (in small groups) 28 h
(4V+2U) 8.0 CP 84 h 156 h

## Basedata

SWS 4V+2U 8.0 CP = 240 h 1 Sem. in WiSe/SuSe  Bachelor (General) [DE] German [MAT-Service] Mathematics for other Departments [NORM] Active

## Possible Study achievement

• Verification of study performance: proof of successful participation in the exercise classes (ungraded)
• Examination number (Study achievement): 81101 ("Higher Mathematics I (prerequisite)")
• Details of the examination (type, duration, criteria) will be announced at the beginning of the course.

## Contents

• Basic concepts and calculation techniques: set theory, real and complex numbers (in particular: Cartesian coordinates and polar coordinates, roots of complex numbers), solving equations and inequalities;
• Functions of one variable: basic concepts and elementary functions, continuity, symmetry, monotony, inverse function, rational functions, asymptotes, sequences and series (limit value concept, calculation rules), power series (convergence behavior and calculation with power series), exponential function and logarithm, trigonometric functions;
• Differentiation (one-dimensional): definition of limit values and significance of derivation, computational techniques, implicit derivation, mean value theorem, extreme values, de l'Hospital rule, Taylor expansion, representation of functions by Taylor series, applications (error estimation and approximation);
• Integration (one-dimensional): definite/indefinite Integral (antiderivative, Riemann sum, main theorem of differential and integral calculus, mean value theorem), integration techniques (substitution, partial integration), integration of power series and rational functions, ideas of numerical integration, improper integrals, various applications.

## Literature

• K. Burg, A. Haf, H. Wille, F. Meister: Höhere Mathematik für Ingenieure,
• G. Bärwolff: Höhere Mathematik für Naturwissenschaftler und Ingenieure,
• T. Rießinger: Mathematik für Ingenieure,
• H. Neunzert, W.G. Eschmann, A. Blickensdörfer-Ehlers, K. Schelkes: Analysis 1.

## Materials

To prepare for the course, participation in the Online Mathematics Bridge Course (OMB+, in German language) is recommended, see https://www.mathematik.uni-kl.de/omb/

## Registration

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

None

None

## References to Course [MAT-00-01-K-1]

Module Name Context
[EIT-BM1-M-2] Mathematisch-naturwissenschaftliche Grundlagen P: Obligatory in Obligatory-Modulteil #A (Höhere Mathematik I) 4V+2U, 8.0 LP
[MAT-00-01-M-1] Higher Mathematics I P: Obligatory 4V+2U, 8.0 LP
[MV-BEMT-1-M-2] Higher Mathematics P: Obligatory 4V+2U, 8.0 LP
[MV-FDT-B139-M-2] Higher Mathematics P: Obligatory 4V+2U, 8.0 LP