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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 Spring '08
 Neely
 Linear Algebra, ax, Mathematica, Diagonal matrix

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