## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Course MAT-10-12-K-2

## Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes and tutorials (V/U/T) 13.0 CP 264 h
6 V Lecture 84 h
2 U Exercise class (in small groups) 28 h
1 T Tutorial 14 h
(6V+2U+1T) 13.0 CP 126 h 264 h

## Basedata

SWS 6V+2U+1T 13.0 CP = 390 h 1 Sem. in WiSe/SuSe [2] Bachelor (Fundamentals) [DE] German [MAT-GRU] Mathematics (B.Sc. year 1 and 2) [NORM] Active

## Possible Study achievement (Übungsschein Grundlagen der Mathematik II)

• Verification of study performance: proof of successful participation in the exercise classes (incl. written examination)
• Examination number (Study achievement): 82016 ("Exercise Class Fundamentals of Mathematics II")
Qualified proof of successful participation in the exercise classes requiring active participation in the exercises, successful completion of homework and passing the final exam for the exercise classes.

## Contents

• basic topological terms (metric spaces, connectedness, compactness),
• differentiation (in the multi-dimensional case) - in particular: Taylor expansion, curves, implicit functions theorem, inverse function theorem, extremes under constraints,
• integration (multi-dimensional) - in particular: Fubini's theorem, variable transformation,
• geometry of Euclidean space (especially: orthogonal transformations, projections),
• eigenvalues, diagonalisability, principal axis transformation, calculation of the Jordan normal form,
• dual space.

## Literature

• O. Forster: Analysis 2,
• H. Heuser: Lehrbuch der Analysis, Teil 2,
• M. Barner, F. Flohr: Analysis II,
• K. Königsberger: Analysis 2,
• G. Fischer: Lineare Algebra,
• K. Jänich: Lineare Algebra,
• H.-J. Kowalsky, G.O. Michler: Lineare Algebra,
• S. Bosch: Lineare Algebra.

## 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).

None

## References to Course [MAT-10-12-K-2]

Module Name Context
[MAT-10-12P-M-2] Fundamentals of Mathematics II (for Students of Physics) P: Obligatory 6V+2U+1T, 13.0 LP
[MAT-10-1-M-2] Fundamentals of Mathematics P: Obligatory in Obligatory-Modulteil #B (Fundamentals of Mathematics II) 6V+2U+1T, 13.0 LP
[PHY-M1-M-2] Fundamentals of Mathematics (for Physics) P: Obligatory in Obligatory-Modulteil #B (Grundlagen der Mathematik II) 6V+2U+1T, 12.0 LP