Functional Analysis For Physics And Engineering

A theory is the more impressive, the simpler are its premises, the more distinct are the things it connects, and the broader is its range of applicability. Albert Einstein There are two different ways of teaching mathematics, namely, (i) the systematic way, and (ii) the application-oriented way.

This book familiarizes readers with the practical application of the numerical simulation technique to solve complex analytical problems in different industries and sciences.

Originally, functional analysis was that branch of mathematics capable of investigating in an abstract way a series of linear mathematical models from science. The study of these linear models—in fact, only first approximations of real models—proved insufficient, so the theory had to be extended to be able to describe the nonlinear phenomena themselves. In this way nonlinear functional analysis was born and continues to develop, becoming a vast and fascinating field of mathematics, with deep applications to increasingly complex problems in physics, biology, chemistry, and economics.

The invited papers in this volume provide a detailed examination of Clifford algebras and their significance to geometry, analysis, physics, and engineering. Divided into five parts, the book's first section is devoted to Clifford analysis; here, topics encompass the Morera problem, inverse scattering associated with the Schrödinger equation, discrete Stokes equations in the plane, a symmetric functional calculus, Poincaré series, differential operators in Lipschitz domains, Paley-Wiener theorems and Shannon sampling, Bergman projections, and quaternionic calculus for a class of boundary value problems.

A theory is the more impressive, the simpler are its premises, the more distinct are the things it connects, and the broader is its range of applicability. Albert Einstein There are two different ways of teaching mathematics, namely, (i) the systematic way, and (ii) the application-oriented way.