Higher Analysis MST.HAN mstm2 2 V 1 U 1 F 5 0 no German Written exam/paper MTM.HAN Mechatronics 0 optional course MST.HAN Mechatronics and Sensor Technology 0 optional course MST.HAN Mechatronics and Sensor Technology 0 optional course 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. Prof. Dr. Barbara Grabowski bg Prof. Dr. Barbara Grabowski bg After successfully completing this course, students will be able to investigate force and velocity fields and other fields of physics and electrical engineering using vector analysis methods. In addition, they will be able to describe curves and curved surfaces in R2 and R3 parametrically using curvilinear coordinate systems and calculate properties such as lengths, curvatures, areas, volumes and centers of gravity, solve complex applied extreme value problems for functions in several variables with and without constraints, and handle eigenvalues, eigenvectors, and quadrics in practical applications. 1. Curves as vector-valued functions in a variable 1.1 Definition of vector functions and their geometrical meaning 1.2 Differentiation and integration of curves, Jordan curves 1.3 Tangent vectors and orientation of a curve 1.4 Case studies: Applications 2. Real-value functions in several variables 2.1 Definition, surfaces of revolution and planes 2.2 The directional derivatives, partial derivatives and their properties 2.4 The gradient, tangent plane and total differential 2.5 Extreme value search methods with and without auxiliary conditions 2.6 Case studies: practical applications 3. Coordinate transformation _ Curvilinear coordinates 3.1 The Jacobi matrix and its determinants 3.2 Coordinate lines and bases in curvilinear coordinate systems 3.3 Spherical, cylindrical and polar coordinates 3.4 Multiple integrals and integral transform 3.5. Case studies: practical applications 4. Scalar and vector fields 4.1 Definitions 4.2 Gradient of a scalar field, rotation and divergence of vector fields and their meaning 4.3 Potential fields and potential function 4.4 Del and Laplace operator and useful equations - Maxwell"s equations 4.5 Line, surface and volume integrals over scalar and vector fields and their physical meaning 4.6. Theorems of Gauss and Stokes 4.7 Case studies: applications 5. Eigenvalues and eigenvectors, quadrics 5.1 Scalar products and orthogonality 5.2. Orthogonal matrices, orthogonal bases, change between orthogonal bases 5.3. Eigenvalues and eigenvectors, eigenvalue estimation 5.4. EWe and EVe of symmetrical matrices, principal axis transformation (diagonalizability of a matrix) 5.5 Square shapes 5.6 Positive/negative (semi) definite matrices 5.7. Quadrics, normal form in R^2 and R^3 5.8 Case studies: practical applications Projector, smart notebook, lecture notes PC lab: AMSeL Papula: Mathematik für Ingenieure und Naturwissenschaftler, Band 1-3, Vieweg 2000. MARSHDEN, TROMBA: Vektoranalysis, Spektrum, 1995. Bourne, Kendall: Vektoranalysis, Teubner, 1966. J.Stoer, R. Bulirsch "Einführung in die Numerische Mathematik I und II", Springer; Auflage: 5. Aufl. 2005 Springer; Auflage: 10., neu bearb. 2007. D. Wille "Repetitorium der Linearen Algebra, Teil 1" Binomi 1997. D. Wille, M. Holz "Repetitorium der Linearen Algebra, Teil 2" Binomi Verlag; Auflage 2, 2006. G.Merziger, T. Wirth "Repetitorium der höheren Mathematik" Binomi; Auflage 5, 2006. B.Griese "Übungsbuch zur Linearen Algebra: Aufgaben und Lösungen" Vieweg+Teubner Verlag; Auflage 7, überarb. u. erw. Aufl. 2011. K.Jänich "Lineare Algebra" Springer; 11. Aufl. 2008. 2., korr. Nachdruck 2013. Mon Oct 25 16:06:19 CEST 2021, CKEY=yha, BKEY=mstm2, CID=[?], LANGUAGE=en, DATE=25.10.2021