Nonlinear Functional Analysis and its Applications: I: Fixed-Point Theorems

"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 mathematically, 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 measurements; behavior of magnetic fields of astrophysical objects; melting processes; chemical reactions; heat radiation; processes in nuclear reactors; nonlinear oscillation in physics, chemistry, and biology; 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 measurements on the body surface to prevent heart attacks; determining material constants or material laws.