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Mathematics 2

Module name (EN):
Name of module in study programme. It should be precise and clear.
Mathematics 2
Degree programme:
Study Programme with validity of corresponding study regulations containing this module.
Applied Informatics, Bachelor, ASPO 01.10.2011
Module code: PIB215
SAP-Submodule-No.:
The exam administration creates a SAP-Submodule-No for every exam type in every module. The SAP-Submodule-No is equal for the same module in different study programs.
P221-0002
Hours per semester week / Teaching method:
The count of hours per week is a combination of lecture (V for German Vorlesung), exercise (U for Übung), practice (P) oder project (PA). For example a course of the form 2V+2U has 2 hours of lecture and 2 hours of exercise per week.
4V+2U (6 hours per week)
ECTS credits:
European Credit Transfer System. Points for successful completion of a course. Each ECTS point represents a workload of 30 hours.
7
Semester: 2
Mandatory course: yes
Language of instruction:
German
Assessment:
Written examination

[updated 08.05.2008]
Applicability / Curricular relevance:
All study programs (with year of the version of study regulations) containing the course.

PIB215 (P221-0002) Applied Informatics, Bachelor, ASPO 01.10.2011 , semester 2, mandatory course
Workload:
Workload of student for successfully completing the course. Each ECTS credit represents 30 working hours. These are the combined effort of face-to-face time, post-processing the subject of the lecture, exercises and preparation for the exam.

The total workload is distributed on the semester (01.04.-30.09. during the summer term, 01.10.-31.03. during the winter term).
90 class hours (= 67.5 clock hours) over a 15-week period.
The total student study time is 210 hours (equivalent to 7 ECTS credits).
There are therefore 142.5 hours available for class preparation and follow-up work and exam preparation.
Recommended prerequisites (modules):
PIB125 Mathematics 1


[updated 01.04.2006]
Recommended as prerequisite for:
PIB315 Mathematics 3
PIBWI19 Machine Learning
PIBWI83 Computer Vision
PIBWI92 Numerical Software


[updated 02.03.2017]
Module coordinator:
Prof. Dr. Rainer Lenz
Lecturer:
Prof. Dr. Rainer Lenz


[updated 06.10.2010]
Learning outcomes:
Students will be taught the basic mathematical skills needed to understand the basic subjects dealt with in phase I of the bachelor programme and the specialist subjects treated in phase II.

[updated 08.05.2008]
Module content:
1        Differential calculus
1.1        The concept of derivative, rules of differential calculus
1.2        Properties of differentiable functions
1.3        Higher derivatives
1.4        Monotony and convexity
 
2        Curve tracing
 
3        Extrema problems
 
4        Integral calculus
4.1        Riemann sums, the definite integral
4.2        Indefinite integrals, the Fundamental Theorem of Calculus
4.3        Methods of integration: partial integration, substitutions rules, decomposition into partial fractions
 
5        Plane curves
5.1        Parametric representation and polar forms
5.2        Tangents, normals, curvature, vertices
5.3        Metric properties: computation of area and arc length
 
6        Power series
6.1        Properties, convergence range
6.2        Taylor series, expansions for standard functions
6.3        Series expansion techniques
 
7        Working with complex numbers
 
8        Multivariate functions
8.1        Representing multivariate functions, level curves
8.2        Partial derivatives, differentiability
8.3        Directional derivative, gradient
8.4        Chain rules
8.5        Extrema problems, extrema with auxiliary conditions
8.6        Envelopes of families of curves
8.7        Multiple integrals
 
9        Ordinary differential equations
9.1        First-order ODEs: separation of variables, linear ODEsSecond-order ODEs with constant coefficients


[updated 08.05.2008]
Recommended or required reading:
Hartmann, P.:  Mathematik für Informatiker, Vieweg, 3.Aufl. 2004
Meyberg, K. Vachenauer, P.:  Höhere Mathematik 1, Springer
Fetzer, A. Fränkel, H.:  Mathematik 1, Springer
Fetzer, A. Fränkel, H.:  Mathematik 2, Springer


[updated 08.05.2008]
Module offered in:
SS 2017, SS 2016, SS 2015, SS 2014, SS 2013, ...
[Thu Jun 20 11:15:38 CEST 2024, CKEY=pmathe2, BKEY=pi, CID=PIB215, LANGUAGE=en, DATE=20.06.2024]