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Mathematics II

Module name (EN): Mathematics II
Degree programme: Electrical Engineering, Bachelor, ASPO 01.10.2005
Module code: E201
Hours per semester week / Teaching method: 4V+2U (6 hours per week)
ECTS credits: 8
Semester: 2
Mandatory course: yes
Language of instruction:
German
Assessment:
Written examination
Curricular relevance:
E201. Biomedical Engineering, Bachelor, ASPO 01.10.2011, semester 2, mandatory course, course inactive since 28.11.2013
E201 Electrical Engineering, Bachelor, ASPO 01.10.2005, semester 2, mandatory course
Workload:
90 class hours (= 67.5 clock hours) over a 15-week period.
The total student study time is 240 hours (equivalent to 8 ECTS credits).
There are therefore 172.5 hours available for class preparation and follow-up work and exam preparation.
Recommended prerequisites (modules):
E101 Mathematics I


[updated 10.03.2010]
Recommended as prerequisite for:
E301 Mathematics III
E404 Electric Power Supply Systems I
E405 Electrical Machines I
E410 Signal and Systems Theory
E412 Fundamentals of Transmission Technology
E506 Building Services Engineering I
E513 High-Voltage Engineering I
E515 Communications Engineering
E518 High-Frequency Engineering


[updated 13.03.2010]
Module coordinator:
Prof. Dr. Wolfgang Langguth
Lecturer:
Prof. Dr. Wolfgang Langguth
Prof. Dr. Barbara Grabowski
Prof. Dr. Harald Wern


[updated 10.03.2010]
Learning outcomes:
After successfully completing this course, students will have acquired a broader knowledge of differential and integral calculus and the skills necessary to handle problems in these areas. Students will learn to use Taylor series for a variety of qualitative approximations relevant to a range of problems in electrical engineering. They will also be introduced to the concept of Fourier series and will acquire the necessary techniques to use them to describe periodic processes. After learning about different types of solutions to second-order differential equations and having acquired the skills needed to solve such equations, students will be able to analyse the basic temporal behaviour of elementary and complex systems arising in different areas of electrical engineering.

[updated 10.03.2010]
Module content:
1.Differential calculus
 1.1.The concept of derivative
 1.2.Basic rules of differentiation
 1.3.Derivatives of elementary functions
 1.4.The differential of a function
 1.5.The mean value theorem of differential calculus
 1.6.Computing boundary values
 
2.Integral calculus
 2.1.Indefinite integrals
 2.2.Definite integrals
 2.3.The application of integral calculus in geometry
 2.4.Techniques of integration
 2.5.Applications of integral calculus
 2.6.Numerical integration
 2.7.Improper integrals
 
3.Infinite series
 3.1.Series with constant terms
 3.2.Sequences and series of functions
 3.3.Power series
 3.4.Taylor series
 3.5.Fourier series
 
4.Differential equations (DEs)
 4.1.Basic terminology
 4.2.First-order differential equations
  4.2.1.Geometrical interpretation
  4.2.2.First-order DEs with separable variables
  4.2.3.Integration of a differential equation by substitution
  4.2.4.Linear first-order DEs
  4.2.5.Linear first-order DEs with constant coefficients
 4.3.Second-order DEs that can be reduced to first-order DEs
  4.3.1.Linear first-order DEs with constant coefficients
  4.3.2.Definition of a linear DE with constant coefficients
  4.3.3.Properties of linear DEs
  4.3.4.Homogeneous linear second-order DEs
  4.3.5.Inhomogeneous second-order DEs


[updated 10.03.2010]
Teaching methods/Media:
Blackboard, overhead projector, video projector, lecture notes (planned)

[updated 10.03.2010]
Recommended or required reading:
PAPULA: Mathematik für Ingenieure und Naturwissenschaftler, Band 1-3, Vieweg, 2000
BURG, HAF, WILLE: Höhere Mathematik für Ingenieure, Band 1-3, Teubner, 2003
BRAUCH, DREYER, HAACKE: Mathematik für Ingenieure, Teubner, 2003
DÜRRSCHNABEL: Mathematik für Ingenieure, Teubner, 2004
DALLMANN, ELSTER: Einführung in die höhere Mathematik I-III, Gustav Fischer, 1991
PAPULA: Mathematische Formelsammlung für Ingenieure und Naturwissenschaftler, Vieweg, 2000
BRONSTEIN, SEMENDJAJEW, MUSIOL, MÜHLIG: Taschenbuch der Mathematik, Deutsch 2000
STÖCKER: Taschenbuch der Mathematik, Harri Deutsch Verlag, Frankfurt

[updated 10.03.2010]
[Sat Jan 23 20:30:11 CET 2021, CKEY=emia, BKEY=e, CID=E201, LANGUAGE=en, DATE=23.01.2021]