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matheng_octave - Advanced Mathematics for Engineers Part 1...

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Advanced Mathematics for Engineers Part 1 Wolfgang Ertel translated by Elias Drotleff and Richard Cubek December 19, 2011
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Preface The first version of this script was created in the winter semester 95/96. I have covered in this lecture only Numerics, although I wanted to cover initially Discrete Mathematics too, which is very important for computer scientists. If you want to cover both in a lecture of three semester week hours, it can happen only superficially. Therefore I decided to focus like my colleagues on Numerics. Only then it is possible to impart profound knowledge. The lecture starts with an introduction to Mathematica. Mathematica is a functional pro- gramming language with an extensive program library for numerical analysis and symbol processing, and graphics. Therewith a powerful tool is provided for the Exercises. From Numerical Analysis besides the basics, system of linear equations, various interpolation methods of measured values and function approximation, and root calculation of nonlinear functions will be presented. An excursion into applied research follows, where e.g. in the field of benchmarking of Microprocessors, mathematics (functional equations) is influencing directly the practice of computer scientists. I want to thank Mr A. Rehbeck for creating the very first version of this script, with a lot of commitment, patience and L A T E Xout of his lecture notes. In summer 1998 a chapter about Statistics was added, because of the weak coverage at our University till then. In the winter semester 1999/2000, the layout and structure were improved, as well some mistakes have been removed. In the context of changes in the summer semester 2002 in the study regulation of Applied Computer science, statistics was shifted, because of the general relevance for all students, into the lecture Mathematics 2. Instead of Statistics, contents should be included, which are specifically relevant for computer scientists. The generation and verification of random numbers is an important topic, which is finally also covered. Since summer 2008, this lecture is only offered to Master (Computer Science) students. Therefore the chapter about random numbers was extended. Maybe other contents will be included in the lecture. For some topics original literature will be handed out, then student have to prepare the material by themselves. To the winter semester 2010/11 the lecture has now been completely revised, restructured and some important sections added such as radial basis functions, Gaussian processes and statistics and probability. These changes become necessary with the step from Diploma to Master. The lecture will now be given to master students from computer science, mecha- tronics and electrical engineering. I am happy to have Markus Schneider and Haitham Bou Ammar as excellent additional lecturers. Their parts really improve the lecture and I am looking forward to interesting semesters with many motivated and eager students who want to climb up the steep, high and fascinating mountain of engineering mathematics together with us. I assure you that we will do our best to guide you through the sometimes wild,
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