Introduction to Functional Analysis and Its Applications

Author: Shi Bao, Wang Xingping, Gai Mingjiu, Zhang Decun / Country: Mainland China
Publisher:
Publish Date: 2006-08-01
Features: This book provides a detailed introduction to the fundamental theories and applications of functional analysis, building upon the reader's existing knowledge of calculus and linear algebra. It covers the theoretical foundations of k-Besgue measure and Lebesgue integration; basic concepts of metric spaces; fundamental concepts of normed linear spaces and Banach spaces; basic theories of Banach spaces; fixed-point theorems and their applications; basic concepts and theories of inner product spaces and Hilbert spaces; the theory of the spectrum of linear operators; the theoretical foundations of nonlinear operators and calculus in Banach spaces; the method of upper and lower solutions and their applications, as well as the theory of topological degree and its applications. This book is suitable for senior undergraduate students in mathematics majors (including joint training programs in mathematics for military academies) and master's or doctoral students in science and engineering disciplines for study and research. It can also serve as a reference for college teachers in teaching and scientific research.