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.