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MEDI  Mathematics II Course INF
Lecturers : Prof. Dr. Roland Uhl    eMail
Term 2
Course Classification : Medizininformatik CH 4
Language : Deutsch Type VÜ 
Type of examination : PL  Credits 5 
Method of evaluation : written examination 120 min 
Requirements :
Cross References :  
Previous knowledges : Mathematics I 
Aids and special features :  
Teaching aims : Ability to do matrix calculations: equivalent transformations, application of Gauß algorithm;
confident complex arithmetic: arithmetic, trigonometric and Euler representation, calculation with complex numbers,
ability to compute determinants, invert matrices and to determine the rank of matrices, solving of linear systems, identification of eigenvalues and eigenvectors;
ability to understand and apply definitions of basic notions of vector arithmetic, ability to test n-dimensional vectors for linear independency and dependency
working knowledge of definitions, properties and application of the inner product, the vector product and mixed product
ability to describe lines and planes by equations and to compute meets, distances and angles
knowledge of how to compute translations, rotations and scalings, how to transform one coordinate system into another one.  
Contents :

Linear systems I: homogeneous and heterogeneous systems, matrices, equivalence of matrices, Gauß algorithm, theorems on solutions of linear systems;
algebraic structures with two operations: rings and fields, complex numbers, fundamental theorem of algebra
Linear systems II: determinants, Laplace rule, rank of a matrix, Cramer rule, inverse of square matrix, Determinantensatz, structure and geometrical representation of solution sets, direction angles and distances of lines and planes, meets of solution sets;
Vector spaces and linear maps: definition, linear independence, bases and subspaces, representation of vectors, linear maps, transformation of bases, Eigenvalues and Eigenvectors;
Euclidean spaces: inner product, dihedral angles, Gram Schmidt process for orthogonalisation 

Literature : Teschl, G. Teschl. S.: Mathematik für Informatiker - Band 1. Diskrete Mathematik und Lineare Algebra, Springer, Berlin; Auflage: 1 (Januar 2006).
Fetzer, A., Fränkel. H(Hrg): Mathematik I, Lehrbuch für Fach-hochschulen, Band 1, Springer, Berlin, 2004.
Stingl, P. Mathematik für Fachhochschulen, Hanser Fachbuch; Auflage: 5. vollst. neubearb. Aufl. (1996).
Burg, K., Haf H., Wille, F.: Höhere Mathematik für Ingenieure Band II, Lineare Algebra, Teubner Verlag; Auflage: 4. Aufl. (12. Februar 2002) .
Pforr, E., Oehlschlägel, L., Seltmann, G.: Übungsaufgaben zur linearen Algebra und linearen Optimierung Ü3, B.G. Teubner Verlag; Auflage: 5. Aufl. (1. Januar 1998). 

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