- 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.

# Module MAT-10-12P-M-2

## Fundamentals of Mathematics II (for Students of Physics) (M, 13.0 LP)

## Module Identification

Module Number | Module Name | CP (Effort) |
---|---|---|

MAT-10-12P-M-2 | Fundamentals of Mathematics II (for Students of Physics) | 13.0 CP (390 h) |

## Basedata

CP, Effort | 13.0 CP = 390 h |
---|---|

Position of the semester | 1 Sem. in WiSe/SuSe |

Level | [2] Bachelor (Fundamentals) |

Language | [DE] German |

Module Manager | |

Lecturers | |

Area of study | [MAT-Service] Mathematics for other Departments |

Reference course of study | [PHY-82.128-SG] B.Sc. Physics |

Livecycle-State | [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. | |
---|---|---|---|---|---|---|---|---|---|---|

6V+2U+1T | MAT-10-12-K-2 | Fundamentals of Mathematics II
| P | 126 h | 264 h |
qU-Schein
| - | PL1 | 13.0 | WiSe/SuSe |

- About [MAT-10-12-K-2]: Title: "Fundamentals of Mathematics II"; Presence-Time: 126 h; Self-Study: 264 h
- About [MAT-10-12-K-2]:
The study achievement
**"[qU-Schein] proof of successful participation in the exercise classes (incl. written examination)"**must be obtained.

## Examination achievement PL1

- Form of examination: oral examination (20-30 Min.)
- Examination Frequency: each semester

## Evaluation of grades

The grade of the module examination is also the module grade.

## Contents

## Competencies / intended learning achievements

Upon successful completion of this module, the students

- know and understand the basic concepts, propositions and methods of Linear Algebra and multi-dimensional Analysis; through the exercises and the tutorials they have acquired a confident, precise and independent handling of the terms, statements and methods dealt with in the lectures;
- recognise the connections between the areas of Linear Algebra and Analysis;
- are trained in analytical thinking; they are able to recognise abstract structures and to work on mathematical problems imaginatively;
- have learned, on the basis of a proof- and structure-oriented approach, to comprehend mathematical proofs and to independently prove or disprove mathematical statements in simple examples;
- are able to convey elementary mathematical facts; their teamwork and communication skills have been trained through exercises and tutorials.

## 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 and tutorials via the online administration system URM (https://urm.mathematik.uni-kl.de).

## Requirements for attendance of the module (informal)

#### Modules:

## Requirements for attendance of the module (formal)

Proof of successful participation in the exercise classes of "Fundamentals of Mathematics I" is prerequisite for participation in the module examination.

## References to Module / Module Number [MAT-10-12P-M-2]

Course of Study | Section | Choice/Obligation |
---|---|---|

[PHY-82.128-SG] B.Sc. Physics | [Fundamentals] Mathematikmodule | [P] Compulsory |