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Higher Mathematics II (Numerical Methods and Statistics)

Module name (EN): Higher Mathematics II (Numerical Methods and Statistics)
Degree programme: Electrical Engineering, Master, ASPO 01.10.2005
Module code: E806
Hours per semester week / Teaching method: 3V+1U (4 hours per week)
ECTS credits: 5
Semester: 8
Mandatory course: yes
Language of instruction:
German
Assessment:
Written exam

[updated 12.03.2010]
Applicability / Curricular relevance:
E806 Electrical Engineering, Master, ASPO 01.10.2005, semester 8, mandatory course
Workload:
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):
E801 Higher Mathematics I (Vector analysis)


[updated 12.03.2010]
Recommended as prerequisite for:
E934 Partial Differential Equations and Function Theory
E938 Statistics II


[updated 09.12.2013]
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:
Statistical and numerical methods play a major role in engineering, particularly in the field of mechatronics. They are important when designing experiments and analysing and evaluating observation data, as well as for modelling, simulating and optimizing processes, and when attempting to identify and model interdependencies. Basic aspects of statistics and probability calculus are also required in determining the correct results in many electrical and electronic engineering applications.
After completing this module, students will be in a position to tackle complex statistical and numerical problems of practical relevance by applying the appropriate methods and techniques working individually or in collaboration with mathematicians.

[updated 12.03.2010]
Module content:
I. Numerical Methods
 
1.Introduction and fundamental principles
2.Solving systems of linear equations
  a.Direct methods
  b.Iterative techniques
3.Polynomial approximation, interpolation
4.Nonlinear equations
5.Numerical differentiation
6.Differential equations
 
II. Statistics
 
1.Descriptive statistics
 1.1 Analysing observation data
 1.2 Metrics for describing relationships between observed features
 
2.Fundamentals of probability theory
 2.1 Definition of probability
 2.2 Discrete and continuous random variables and their distributions
 2.3 Special continuous and discrete distributions
 2.4 The reproductive and limit theorems and their applications
 
3.Applications of statistics in engineering
 3.1 Estimating probabilities, mean values and variances; tolerance ranges
 3.2 Statistical quality control
 3.3 Experiment design, determining the observation range, choice of key  
     parameters
 3.4 Regression and correlation analysis
 3.5 Time series analysis
 3.6 Variance analysis
 
4.Introduction to R
 4.1 Small-scale projects
 


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

[updated 12.03.2010]
Recommended or required reading:
SCHWARZ: Numerische Mathematik, Teubner, 1993
Scheid: Numerische Analysis, Schaum, 1991
Press et al. : Numerical Recipes, Cambridge Press, 1987
STOER: Einführung in die Numerische Mathematik I und II, Springer, 1972
Schwetlick, Kretschmar: Numerische Verfahren für Naturwissenschaftler und Ingenieure, Fachbuchverlag Leipzig, 1991
SCHABACK, WERNER: Numerische Mathematik, Springer, 1992
KOSE, SCHRÖDER, WIELICZEK: Numerik sehen und verstehen, Vieweg, 1992
Lehn, Wegmann: Einführung in die Statistik, Teubner, 2004
PAPULA: Mathematik für Ingenieure und Naturwissenschaftler, Band 1-3, Vieweg, 2000.
Brigham: FFT-Anwendungen, Oldenburg Verlag 1997
B. Grabowski:  Statistik  für Ingenieure technischer Fachrichtungen an Fachhochschulen,
e-Lerning-Buch in ACTIVEMATH.
H.Weber: Einführung in die Wahrscheinlichkeitsrechnung
 
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
Material available at www.htw-saarland.de/fb/gis/mathematik:
1) Lecture notes I and II  (Internet)
2) Formula sets 1 and 2 to lecture notes I and II
3) Exercises and worked solutions to problems in lecture notes I and II
4) Online e-learning server ACTIVEMATH

[updated 12.03.2010]
[Sat Jul  2 21:55:39 CEST 2022, CKEY=ehmixus, BKEY=em, CID=E806, LANGUAGE=en, DATE=02.07.2022]