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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 TheoryE938 Statistics II [updated 09.12.2013] Module coordinator: Prof. Dr. Wolfgang Langguth Lecturer: Prof. Dr. Wolfgang LangguthProf. Dr. Barbara GrabowskiProf. 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 principles2.Solving systems of linear equations  a.Direct methods  b.Iterative techniques3.Polynomial approximation, interpolation 4.Nonlinear equations5.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, 1993Scheid: Numerische Analysis, Schaum, 1991Press et al. : Numerical Recipes, Cambridge Press, 1987STOER: Einführung in die Numerische Mathematik I und II, Springer, 1972Schwetlick, Kretschmar: Numerische Verfahren für Naturwissenschaftler und Ingenieure, Fachbuchverlag Leipzig, 1991SCHABACK, WERNER: Numerische Mathematik, Springer, 1992KOSE, SCHRÖDER, WIELICZEK: Numerik sehen und verstehen, Vieweg, 1992Lehn, Wegmann: Einführung in die Statistik, Teubner, 2004PAPULA: Mathematik für Ingenieure und Naturwissenschaftler, Band 1-3, Vieweg, 2000.Brigham: FFT-Anwendungen, Oldenburg Verlag 1997B. 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, 2000BRONSTEIN, SEMENDJAJEW, MUSIOL, MÜHLIG: Taschenbuch der Mathematik, Deutsch 2000STÖCKER: Taschenbuch der Mathematik, Harri Deutsch Verlag, FrankfurtMaterial 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 II3) Exercises and worked solutions to problems in lecture notes I and II 4) Online e-learning server ACTIVEMATH [updated 12.03.2010]
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