|Module code: PIB-MA2
3V+1U (4 hours per week)|
|Mandatory course: yes
|Language of instruction:
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
Prof. Dr. Peter Birkner
|Lecturer: Prof. Dr. Peter Birkner
_ 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.
Sequences and series
Supremum, infimum, limits, limit theorems
Series, direct comparison test and ratio test
Geometric series, exponential series
Properties of continuous functions
Inverse functions, logarithms, inverse trigonometric functions
Concept of derivation, calculation rules
Properties of differentiable functions
Monotonicity and convexity
Applications such as Hospital´s rule, extreme value tasks and Taylor series
Riemann sums, definite integral
Indefinite integral, fundamental theorem of calculus
Integration methods: partial integration, substitution rule
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.
|Recommended or required reading:
- P. Hartmann, Mathematik für Informatiker (Vieweg); can be downloaded via OPAC as a PDF.
- M. Brill, Mathematik für Informatiker (Hanser).
|Module offered in: |