The course continues the topics in calculus of a single variable. Infinite sequences, series and series expansions like Taylor and Maclaurin expansions are the basis of approximations and solution strategies for first and second order differential equations. The next step is to generalize the framework of calculus by general concepts from linear algebra. The basic elements like vectors and matrices are introduced.

Applications of these objects are discussed to represent linear systems of equations. The different solution strategies for linear systems of equations are presented and the advantages of the solution approaches shown. Based on these techniques the general structure of a linear vector space is introduced and consequences derived for the solution strategies. In addition linear transformations, eigenvalues, eigenvectors as well as the spectral theorem are used in applications. The theoretical structure of linear vector spaces is extended to functions and applications for linear difference and differential equations.

The German University in Cairo, GUC, is an Egyptian Private University founded by the presidential decree 27/2002, according to the law number 101/1992 and its executive regulations number 355/1996.

German university in Cairo/Deutsche Universität in Kairo has been established in 2002 in cooperation with the State Universities of Ulm and Stuttgart, under the patronage of the Egyptian Ministry of Higher Education, the Ministry of Science, Research and Arts, State of Baden- Württemberg, Germany, and supported by the German Academic Exchange Service (DAAD), the German Embassy in Cairo, the Arab/German Chamber of Industry and Commerce (AHK), the Federal Ministry of Education and Research, Germany, The State University of Tübingen and The State University of Mannheim.

The German University in Cairo is an independent, non-profit oriented Egyptian private institution, managed by a consortium of Germans and Egyptians with the vision of building a leading center of excellence in teaching and research that will effectively contribute to the general welfare nationally and internationally and endeavour the scientific, technical, economic and cultural cooperation between Egypt and Germany.

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