Chapter 1 gives an overview of a general projective approximation scheme for operator equations, which covers several well-known approximation methods as special cases, such as the Galerkin-type methods, collocation-like methods, and least-squares-based methods. Chapter 2 discusses approximate solutions of compact linear operator equations, and Chapter 3 studies both classical and generalized solutions, as well as the projective approximations, for general linear operator equations. Chapter 4 gives an introduction to some important concepts, such as the topological degree and the fixed point principle, with applications to projective approximations of nonlinear operator equations. Linear and nonlinear monotone operator equations and their projective approximations are investigated in Chapter 5, while Chapter 6 addresses basic questions in discrete and semi-discrete projective approximations for two important classes of abstract operator evolution equations.

Each chapter contains well-selected examples and exercises, for the purposes of demonstrating the fundamental theories and methods developed in the text and familiarizing the reader with functional analysis techniques useful for numerical solutions of various operator equations.

Readership: Applied mathematicians, mathematical physicists, numerical analysts and electrical & mechanical engineers.