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Mathematics II

Module name (EN):
Name of module in study programme. It should be precise and clear.
Mathematics II
Degree programme:
Study Programme with validity of corresponding study regulations containing this module.
Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2012
Module code: MST.MA2
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.
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.
Semester: 2
Mandatory course: yes
Language of instruction:
Written exam

[updated 10.05.2021]
Applicability / Curricular relevance:
All study programs (with year of the version of study regulations) containing the course.

MST.MA2 (P231-0054) Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2012 , semester 2, mandatory course
MST.MA2 (P231-0054) Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2011 , semester 2, mandatory course
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 180 hours (equivalent to 6 ECTS credits).
There are therefore 112.5 hours available for class preparation and follow-up work and exam preparation.
Recommended prerequisites (modules):
MST.MA1 Mathematics I

[updated 01.10.2012]
Recommended as prerequisite for:
MST.CVI Computer Vision
MST.ESA Computer-Aided Design of Sensors and Actuators
MST.NSW Numerical Software

[updated 01.10.2012]
Module coordinator:
Lecturer: N.N.

[updated 01.10.2012]
Learning outcomes:
This course is designed to teach the mathematical fundamentals, specifically analysis, required for undergraduate and graduate subjects.

[updated 10.05.2021]
Module content:
1 - Real-valued functions in a variable
1.1… Definition, properties (symmetry, monotonicity, boundedness, zeros)
1.2… Inverse functions, shift and rotation
1.3… Representation in polar and spherical coordinate systems, parameter representations
2 – Sequences of numbers
2.1… Definition, properties (monotonicity, boundedness, alternating)
2.2… Convergence and cluster points, limit theorems
3 – Limits and continuity of functions
3.1… Limit theorems, continuity
3.2… Poles, asymptotes
4 - Special elementary functions and their properties
4.1… Integer functions and polynomials
4.2… Broken rational functions and partial fraction decomposition
4.3… Algebraic functions and root equations
4.4… Exponential and logarithm functions
4.5… Trigonometric functions
4.6… Hyperbolic and area functions
5 - Differential calculus
5.1… Derivative of a function, differential quotient, tangent and total differential
5.2….Differentiation rules
5.3….Applications of differential calculus
6 – Integral calculus
6.1… Definite and indefinite integrals
6.2… Integration techniques
6.3… Numerical integration
6.4… Improper integrals
6.5… Applications of integral calculus
7 - Series
7.1… Basic definitions, properties
7.2….Convergence criteria for series (root, quotient criterion, ...)
7.3….Power series (radius of convergence and interval of convergence)
7.4….Taylor series (Taylor series expansion of special functions and residual element estimation)
7.5….Continuity, differentiability and integrability of function series

[updated 10.05.2021]
Teaching methods/Media:
Practical exercises for the lecture, as well as solving exercises, homework and case studies will be done with the e-learning system MathCoach (AMSEL lab: PC lab: "Angewandte Mathematik, Statistik und eLearning").
In addition, a performance-relevant midterm exam will be written as an online exam using the MathCoach elearning system.

[updated 10.05.2021]
Recommended or required reading:
0. B.Grabowski: "Mathematik II für Ingenieure", ebook with MathCoach, 2011
1. L. Papula : "Mathematik für Ingenieure", Band 1-3 und Formelsammlungen, Vieweg, 2000
2. Engeln-Müllges, Schäfer, Trippler: "Kompaktkurs Ingenieurmathematik". Fachbuchverlag  Leipzig im Carl Hanser Verlag: München/Wien, 1999.
   (only available within the htw)

[updated 10.05.2021]
[Sat Jul 13 10:02:13 CEST 2024, CKEY=ymmathe2, BKEY=mst2, CID=MST.MA2, LANGUAGE=en, DATE=13.07.2024]