Siddiqi A.H. Applied Functional Analysis. Numerical Methods, Wavelet Methods, and Image Processing

Издательство Marcel Dekker, 2004, -569 pp.
Functional analysis was invented and developed in the twentieth century. Besides being an area of independent mathematical interest, it provides many fundamental notions essential for modeling, analysis, numerical approximation and computer simulation processes of real-world problems. As science and technology are increasingly refined and interconnected, the demand for advanced mathematics beyond the basic vector algebra and differential and integral calculus has greatly increased. There is no dispute on the relevance of functional analysis; however, there have been differences of opinion among experts about the level and methodology of teaching functional analysis. In the recent past, its applied nature has been gaining ground. The main objective of this book is to present all those results of functional analysis which have been frequently applied in emerging areas of science and technology. Functional analysis provides basic tools and foundation for areas of vital importance such as optimization, boundary value problems, modeling real-world phenomena, finite and boundary element methods, variational equations and inequalities, and wavelets. Wavelets, formally invented in the mid-eighties, have found significant applications in image processing and partial differential equations.
Metric Spaces and Banach Fixed Point Theorem.
Banach Spaces.
Hilbert Space.
Fundamental Theorems.
Differential and Integral Calculus in Banach Spaces.
Operator Equations and Variational Methods.
Optimization Problems.
Finite Element and Boundary Element Methods.
Variational Inequalities and Applications.
Wavelet Theory.
Wavelet Method for Partial Differential Equations and Image Processing.