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During the first decades after Einstein had developed his Theory of
General Relativity, the main effort was to understand the theory
and verify it experimentically. Meanwhile Genral Relativity is one
of the experimentally best confirmed theories and has become a
powerful tool for the investigation of cosmic processes where
strong gravitational fields are involved.
This book contains 16 contributions from well-known experts giving
a broad overview for non-specialists who want to learn how to
purely academic issues like gravitational wave detectors are now
put into reality.
This book addresses graduate students in the first place and is
meant as a modern compendium to the existing texts on black hole
astrophysics. The authors present in pedagogically written articles
our present knowledge on black holes covering mathematical models
including numerical aspects and physics and astronomical
observations as well. In addition, in their write-up of a panel
discussion the participants of the school address the existence of
black holes consenting that it has by now been verified with
certainty.
In this book we display the fundamental structure underlying
classical electro dynamics, i. e., the phenomenological theory of
electric and magnetic effects. The book can be used as a textbook
for an advanced course in theoretical electrodynamics for physics
and mathematics students and, perhaps, for some highly motivated
electrical engineering students. We expect from our readers that
they know elementary electrodynamics in the conventional (1 +
3)-dimensional form including Maxwell's equations. More over, they
should be familiar with linear algebra and elementary analysis, in
cluding vector analysis. Some knowledge of differential geometry
would help. Our approach rests on the metric-free integral
formulation of the conservation laws of electrodynamics in the
tradition of F. Kottler (1922), E. Cartan (1923), and D. van
Dantzig (1934), and we stress, in particular, the axiomatic point
of view. In this manner we are led to an understanding of why the
Maxwell equa tions have their specific form. We hope that our book
can be seen in the classical tradition of the book by E. J. Post
(1962) on the Formal Structure of Electro magnetics and of the
chapter "Charge and Magnetic Flux" of the encyclopedia article on
classical field theories by C. Truesdell and R. A. Toupin (1960),
in cluding R. A. Toupin's Bressanone lectures (1965); for the exact
references see the end of the introduction on page 11. ."
For this set of lectures we assumed that the reader has a
reasonable back ground in physics and some knowledge of general
relativity, the modern theory of gravity in macrophysics, and
cosmology. Computer methods are present ed by leading experts in
the three main domains: in numerics, in computer algebra, and in
visualization. The idea was that each of these subdisciplines is
introduced by an extended set of main lectures and that each is
conceived as being of comparable 'importance. Therefpre we believe
that the book represents a good introduction into scientific I
computing for any student who wants to specialize in relativity,
gravitation, and/or astrophysics. We took great care to select
lecturers who teach in a comprehensible way and who are, at the
same time, at the research front of their respective field. In
numerics we had the privilege of having a lecturer from the
National Center for Supercomputing Applications (NCSA, Champaign,
IL, USA) and some from other leading institutions of the world;
visualization was taught by a visualization expert from Boeing; and
in com puter algebra we took recourse to practitioners of different
computer algebra systems as applied to classical general relativity
up to quantum gravity and differential geometry.
This book presents a fresh, original exposition of the foundations
of classical electrodynamics in the tradition of the so-called
metric-free approach. The fundamental structure of classical
electrodynamics is described in the form of six axioms: (1)
electric charge conservation, (2) existence of the Lorentz force,
(3) magnetic flux conservation, (4) localization of electromagnetic
energy-momentum, (5) existence of an electromagnetic spacetime
relation, and (6) splitting of the electric current into material
and external pieces.
The first four axioms require an arbitrary 4-dimensional
differentiable manifold. The fifth axiom characterizes spacetime as
the environment in which the electromagnetic field propagates a" a
research topic of considerable interest a" and in which the metric
tensor of spacetime makes its appearance, thus coupling
electromagnetism and gravitation. Repeated emphasis is placed on
interweaving the mathematical definitions of physical notions and
the actual physical measurement procedures.
The tool for formulating the theory is the calculus of exterior
differential forms, which is explained in sufficient detail, along
with the corresponding computer algebra programs. Prerequisites for
the reader include a knowledge of elementary electrodynamics (with
Maxwell's equations), linear algebra and elementary vector
analysis; some knowledge of differential geometry would help.
Foundations of Classical Electrodynamics unfolds systematically at
a level suitable for graduate students and researchers in
mathematics, physics, and electrical engineering.
Computer Simulation and Computer Algebra. Starting from simple
examples in classical mechanics, these introductory lectures
proceed to simulations in statistical physics (using FORTRAN) and
then explain in detail the use of computer algebra (by means of
Reduce). This third edition takes into account the most recent
version of Reduce (3.4.1) and updates the description of
large-scale simulations to subjects such as the 170000 X 170000
Ising model. Furthermore, an introduction to both vector and
parallel computing is given.
REDUCE ist ein Kompaktkurs }ber die Anwendung dieses
Computer-Algebra-Systems. REDUCE ist an den deutschen Universt{ten
weit verbreitet und dient zum symbolischen Rechnen mit dem
Computer, wie es fr}her nur mit Papier und Bleistift unter
Zuhilfenahme eines Handbuchs der Mathematik m-glich war. Studenten
der Informatik, Mathematik, Physik, Chemie, der
Ingenieurwissenschaften u.a. erhalten hier das grundlegende
R}stzeug, das ihnen sp{ter auch das Arbeiten mit anderen
Computer-Algebra-Systemen erleichtern wird. Auch Wissenschaftlern,
die bisher noch nicht symbolisch gerechnet haben, kann dieses Buch
uneingeschr{nkt empfohlen werden.
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