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## Higher Mathematics I (Vector analysis)

 Module name (EN): Higher Mathematics I (Vector analysis) Degree programme: Electrical Engineering, Master, ASPO 01.10.2005 Module code: E801 Hours per semester week / Teaching method: 2V+2U (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: E801 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): 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 LangguthProf. Dr. Barbara GrabowskiProf. 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 Maxwell’s 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 Gauss’ theorem 4.2 Stokes’ 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, 1995SCHARK: Vektoranalysis für Ingenieurstudenten, Harri Deutsch, 1992DALLMANN, ELSTER:  Einführung in die höhere Mathematik II, Gustav Fischer, 1991Bourne, Kendall:  Vektoranalysis, Teubner, 1966PAPULA:  Mathematische Formelsammlung für Ingenieure und Naturwissenschaftler, Vieweg, 2000BRONSTEIN, SEMENDJAJEW, MUSIOL, MÜHLIG:  Taschenbuch der Mathematik, Deutsch 2000STÖCKER:  Taschenbuch der Mathematik, Harri Deutsch Verlag, Frankfurt [updated 12.03.2010]
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