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Mathematics 2

Module name (EN): Mathematics 2
Degree programme: Applied Informatics, Bachelor, ASPO 01.10.2017
Module code: PIB-MA2
SAP-Submodule-No.: P221-0002
Hours per semester week / Teaching method: 3V+1U (4 hours per week)
ECTS credits: 5
Semester: 2
Mandatory course: yes
Language of instruction:
Written exam

[updated 19.02.2018]
Applicability / Curricular relevance:
KIB-MAT2 (P221-0002) Computer Science and Communication Systems, Bachelor, ASPO 01.10.2017, semester 2, mandatory course
PIB-MA2 (P221-0002) Applied Informatics, Bachelor, ASPO 01.10.2017, semester 2, mandatory course
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):
Recommended as prerequisite for:
PIB-MA3 Mathematics 3

[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
  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
[Mon Aug  8 00:38:07 CEST 2022, CKEY=km2, BKEY=pi2, CID=PIB-MA2, LANGUAGE=en, DATE=08.08.2022]