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## Mathematics III / Applied Mathematics

 Module name (EN): Mathematics III / Applied Mathematics Degree programme: Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2011 Module code: MST.MA3 SAP-Submodule-No.: P231-0055 Hours per semester week / Teaching method: 4V+1U (5 hours per week, accumulated) ECTS credits: 6 Semester: 3 Duration: 2 semester Mandatory course: yes Language of instruction: German Assessment: Test + term paper [updated 10.05.2021] Applicability / Curricular relevance: MST.MA3 (P231-0055) Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2012, semester 3, mandatory course MST.MA3 (P231-0055) Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2011, semester 3, mandatory course Workload: 75 class hours (= 56.25 clock hours) over a 15-week period.The total student study time is 180 hours (equivalent to 6 ECTS credits).There are therefore 123.75 hours available for class preparation and follow-up work and exam preparation. Recommended prerequisites (modules): MST.NSW Numerical Software [updated 10.05.2019] Recommended as prerequisite for: MST.CVI Computer VisionMST.TMM Mechanical Engineering and Machine Dynamics [updated 10.05.2019] Module coordinator: N.N. Lecturer: N.N. [updated 01.10.2005] Learning outcomes: The objective of this module is to teach the applied mathematical methods required for engineering disciplines such as control engineering and physics.  In addition, it is designed to teach applied methods of higher mathematics in a problem-oriented manner (in particular numerics and statistics) using practical examples. After successfully completing this module, students will be able to solve minor problems based on given measured data using MATLAB and SIMULINK, and present their solution in writing.Part I    [updated 10.05.2021] Module content:   1 - Ordinary differential equationsĢ        Separable DGĢ        Linear differential equation with constant coefficients of the 1st orderĢ        Linear differential equation with constant coefficients of the 2nd orderĢ        Applications in technology  2 - The Fourier transformĢ        Fourier series for periodic functionsĢ        Fourier series for non-periodic functionsĢ        Applications 3 - The Laplace transformĢ        DefinitionĢ        AlgorithmsĢ        Inverse transformation methods (convolution, partial fraction decomposition)Ģ        Applications 4 ¢ Functions with multiple variablesĢ        Partial derivatives, tangent plane    3.        Coordinate transformations, Ģ        Multiple integrals and integral transform 5 ¢ Introduction to vector analysis   Part II 1.  Introduction to Matlab 1.1 Calculating with vectors and matrices, creating graphics2.  Interpolations (Newton polynomials, Spline functions) 2.1 Mini-project3.  Least squares fitting  3.1 Linear balance functions3.2 Non-linear balanced functions3.3 Mini-project4.  Simple statistical measures for one, two, and more than two characteristics4.1 Mini-project5.  Numerical differentiation and integration - Introduction 5.1 Mini-project6.  Introduction to SIMULINK6.1 Solving initial value problems of ordinary differential equations with SIMULINK 6.2 Mini-project  [updated 10.05.2021] Teaching methods/Media: The numerics part II will take place in the PC lab AMSEL (Angewandte Mathematik, Statistik, eLearning (Room 5306).All 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: Part I0. B.Grabowski:"Mathematik III für Ingenieure", e-book mit MathCoach, 20111. L. Papula : "Mathematik für Ingenieure", Band 1-3 und Formelsammlungen, Vieweg, 20002. Engeln-Müllges, Schäfer, Trippler: "Kompaktkurs Ingenieurmathematik". Fachbuchverlag  Leipzig im Carl Hanser Verlag: München/Wien, 1999.3. Brauch/Dreyer/Haacke, Mathematik für Ingenieure, Teubner, 2003 Part II0. B.Grabowski:  "E-Learning: Numerik mit MathCoach", e-book, 20111. Preuss/Wenisch, Numerische Mathematik, Fachbuchverlag, 20012. Faires/Burden, Numerische methoden, Spektrum Akademischer Verlag, 20003. Gramlich/Werner, Numerische Mathematik mit MATLAB, dpunktverlag, 20004. Beucher, MATLAB und SIMULINK lernen, Addison-Wesley, 20005. Bartsch H.-J., Tachenbuch Mathematischer Formeln, Fachbuchverlag Leipzig, 2003   Materials1. www.htw-saarland.de/fb/gis/people/bgrabowski/vorles/mathe.htm   (only available within the htw)2. www.htw-saarland.de/fb/gis/mathematik/     Script I and formula collection 1 for descriptive statistics   [updated 10.05.2021]
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