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."
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