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Module name (EN):
Mathematics 2 |

Degree programme:
Applied Informatics, Bachelor, ASPO 01.10.2017 |

Module code: PIB-MA2 |

Hours per semester week / Teaching method: 3V+1U (4 hours per week) |

ECTS credits: 5 |

Semester: 2 |

Mandatory course: yes |

Language of instruction: German |

Assessment: Written exam [ updated 19.02.2018] |

Applicability / Curricular relevance: KIB-MAT2 Computer Science and Communication Systems, Bachelor, ASPO 01.10.2017, semester 2, mandatory course PIB-MA2 Applied Informatics, Bachelor, ASPO 01.10.2017, semester 2, mandatory course |

Workload: 60 class hours (= 45 clock hours) over a 15-week period. The total student study time is 150 hours (equivalent to 5 ECTS credits). There are therefore 105 hours available for class preparation and follow-up work and exam preparation. |

Recommended prerequisites (modules): None. |

Recommended as prerequisite for: PIB-MA3 Mathematics 3 PIB-RMA2 [ updated 17.08.2021] |

Module coordinator: Prof. Dr. Peter Birkner |

Lecturer: Prof. Dr. Peter Birkner[ updated 28.09.2016] |

Learning outcomes: _ After successfully completing this module, students will be familiar with the definition of the term _limit_ for sequences and real functions and will have learned to master the use of limit theorems. _ They will know the convergence criteria for series and be able to handle them confidently when checking series for convergence. _ They will be able to explain the importance of series expansion for numerical mathematics and computer science applications. _ Students will be familiar with the properties of exponential and logarithmic functions and be able to deal with them confidently in computer science applications. _ They will know the definition of derivation for functions of a variable as a limit value and will have learned to master the derivation rules for functions of a variable. _ Students will be able to develop solutions for the application of differential calculus (setting limits with _L´Hospital´s rule, extreme value tasks, Taylor series and error estimation). _ They will be familiar with the definition of definite and indefinite integrals for variable functions, as well as be able to develop integration solutions using the integration methods _partial integration_ and _integration by substitution_. _ Finally, they will have learned to master complex numbers in the usual forms for representation. [ updated 24.02.2018] |

Module content: Sequences and series Supremum, infimum, limits, limit theorems Series, direct comparison test and ratio test Geometric series, exponential series Continuity Function limits Properties of continuous functions Inverse functions, logarithms, inverse trigonometric functions Differential calculus Concept of derivation, calculation rules Properties of differentiable functions Higher derivatives Monotonicity and convexity Applications such as Hospital´s rule, extreme value tasks and Taylor series Integral calculus Riemann sums, definite integral Indefinite integral, fundamental theorem of calculus Integration methods: partial integration, substitution rule Complex numbers [ updated 24.02.2018] |

Teaching methods/Media: Lecture at board Every two weeks an exercise sheet will be distributed and then discussed in small groups the following week. In addition, a tutorial will be offered every two weeks for work in small groups. This is voluntary. In the tutorials, students will be able work on exercises themselves (with support from the tutor, if necessary) and ask questions about the lecture material. The tutorial can also be used to fill knowledge gaps. [ updated 26.02.2018] |

Recommended or required reading: - P. Hartmann, Mathematik für Informatiker (Vieweg); can be downloaded via OPAC as a PDF. - M. Brill, Mathematik für Informatiker (Hanser). [ updated 19.02.2018] |

Module offered in: SS 2022, SS 2021, SS 2020, SS 2019, SS 2018 |

[Tue Jan 25 00:23:52 CET 2022, CKEY=km2, BKEY=pi2, CID=PIB-MA2, LANGUAGE=en, DATE=25.01.2022]