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Higher Mathematics I (Vector analysis)

Module name (EN):
Name of module in study programme. It should be precise and clear.
Higher Mathematics I (Vector analysis)
Degree programme:
Study Programme with validity of corresponding study regulations containing this module.
Electrical Engineering, Master, ASPO 01.10.2005
Module code: E801
Hours per semester week / Teaching method:
The count of hours per week is a combination of lecture (V for German Vorlesung), exercise (U for ‹bung), 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.
2V+2U (4 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.
5
Semester: 8
Mandatory course: yes
Language of instruction:
German
Assessment:
Written exam

[updated 12.03.2010]
Applicability / Curricular relevance:
All study programs (with year of the version of study regulations) containing the course.

E801 Electrical Engineering, Master, ASPO 01.10.2005 , semester 8, 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).
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):
None.
Recommended as prerequisite for:
E806 Higher Mathematics II (Numerical Methods and Statistics)
E934 Partial Differential Equations and Function Theory


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


[updated 12.03.2010]
Learning outcomes:
After successfully completing this course, students will have acquired a solid theoretical grounding and the practical skills to apply the methods of vector analysis to studying electromagnetic fields or other fields of relevance in physics. Students will acquire the necessary technical skills for a mathematical understanding of Maxwellís equations.

[updated 12.03.2010]
Module content:
1. The vector function of a real variable
 1.1 The vector function and its geometrical significance
 1.2 Differentiating a vector
 
2. Scalar and vector fields
 2.1 Definition of scalar and vector fields, physical motivation, examples
 2.2 The gradient of a scalar field
 2.3 Divergence and curl of a vector field
 2.4 The del operator
 2.5 The Laplace operator
 2.6 Rules of vector calculus and useful equations
 2.7 Curvilinear coordinates
 
3. Line, surface and volume integrals
 3.1 Line integrals of vector fields
 3.2 Multiple integrals
 3.3 Surface integrals
 3.4 Volume integrals
 
4. Integral theorems
 4.1 Gaussí theorem
 4.2 Stokesí theorem
 
5. Applications
 
6. Galilean and Lorentz transformations
 


[updated 12.03.2010]
Teaching methods/Media:
Blackboard, overhead projector, video projector, lecture notes (planned)

[updated 12.03.2010]
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.
MARSHEDEN, TROMBA:  Vektoranalysis, Spektrum, 1995
SCHARK: Vektoranalysis für Ingenieurstudenten, Harri Deutsch, 1992
DALLMANN, ELSTER:  Einführung in die höhere Mathematik II, Gustav Fischer, 1991
Bourne, Kendall:  Vektoranalysis, Teubner, 1966
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 12.03.2010]
[Tue Feb 27 15:46:09 CET 2024, CKEY=ehmix, BKEY=em, CID=E801, LANGUAGE=en, DATE=27.02.2024]