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The greatest mathematicians, such as Archimedes, Newton, and Gauss,
always united theory and applications in equal measure. Felix Klein
There exists the remarkable possibility that one can master a
subject mathemati cally, without really understanding its essence.
Albert Einstein Don't give us numbers: give us insight A
contemporary natural scientist to a mathematician Numerous
questions in physics, chemistry, biology, and economics lead to
nonlinear problems; for example, deformation of rods, plates, and
shells; behavior of plastic materials; surface waves of fluids;
flows around objects in fluids or gases; shock waves in gases;
movement of viscous fluids; equilibrium forms of rotating fluids in
astrophysics; determination of the shape of the earth through
gravitational measu- ments; behavior of magnetic fields of
astrophysical objects; melting processes; chemical reactions; heat
radiation; processes in nuclear reactors; nonlinear oscillation in
physics, chemistry, and biology; 2 Introduction existence and
stability of periodic and quasiperiodic orbits in celestial
mechanics; stability of physical, chemical, biological, ecological,
and economic processes; diffusion processes in physics, chemistry,
and biology; processes with entropy production, and
self-organization of systems in physics, chemistry, and biology;
study of the electrical potential variation in the heart through
measure ments on the body surface to prevent heart attacks;
determining material constants or material laws (e. g."
The greatest mathematicians, such as Archimedes, Newton, and Gauss,
always united theory and applications in equal measure. Felix Klein
There exists the remarkable possibility that one can master a
subject mathemati cally, without really understanding its essence.
Albert Einstein Don't give us numbers: give us insight A
contemporary natural scientist to a mathematician Numerous
questions in physics, chemistry, biology, and economics lead to
nonlinear problems; for example, deformation of rods, plates, and
shells; behavior of plastic materials; surface waves of fluids;
flows around objects in fluids or gases; shock waves in gases;
movement of viscous fluids; equilibrium forms of rotating fluids in
astrophysics; determination of the shape of the earth through
gravitational measu- ments; behavior of magnetic fields of
astrophysical objects; melting processes; chemical reactions; heat
radiation; processes in nuclear reactors; nonlinear oscillation in
physics, chemistry, and biology; 2 Introduction existence and
stability of periodic and quasiperiodic orbits in celestial
mechanics; stability of physical, chemical, biological, ecological,
and economic processes; diffusion processes in physics, chemistry,
and biology; processes with entropy production, and
self-organization of systems in physics, chemistry, and biology;
study of the electrical potential variation in the heart through
measure ments on the body surface to prevent heart attacks;
determining material constants or material laws (e. g."
This book is the result of two courses of lectures given at the
University of Cologne in Germany in 1974/75. The majority of the
students were not familiar with partial differential equations and
functional analysis. This explains why Sections 1, 2, 4 and 12
contain some basic material and results from these areas. The three
parts of the book are largely independent of each other and can be
read separately. Their topics are: initial value problems, boundary
value problems, solutions of systems of equations. There is much
emphasis on theoretical considerations and they are discussed as
thoroughly as the algorithms which are presented in full detail and
together with the programs. We believe that theoretical and
practical applications are equally important for a genuine
understa- ing of numerical mathematics. When writing this book, we
had considerable help and many discussions with H. W. Branca, R.
Esser, W. Hackbusch and H. Multhei. H. Lehmann, B. Muller, H. J.
Niemeyer, U. Schulte and B. Thomas helped with the completion of
the programs and with several numerical calculations.
Springer-Verlag showed a lot of patience and under standing during
the course of the production of the book. We would like to use the
occasion of this preface to express our thanks to all those who
assisted in our sometimes arduous task."
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