\"《应用泛函分析(第1卷)(英文版)》内容简介：More precisely, by （i）, I mean a systematic presentation of the materialgoverned by the desire for mathematical perfection and completeness ofthe results. In contrast to （i）, approach （ii） starts out from the question\"\"What are the most important applications？\"\" and then tries to answer thisquestion as quickly as possible. Here, one walks directly on the main roadand does not wander into all the nice and interesting side roads.The present book is based on the second approach. It is addressed toundergraduate and beginning graduate students of mathematics, physics,and engineering who want to learn how functional analysis elegantly solvesma hematical problems that are related to our real world azld that haveplayed an important role in the history of mathematics. The reader shouldsense that the theory is being developed, not simply for its own sake, butfor the effective solution of concrete problems.\"

\"Preface Prologue Contents of AMS Volume 109 1 Banach Spaces and Fixed-Point Theorems 1.1 Linear Spaces and Dimension 1.2 Normed Spaces and Convergence 1.3 Banach Spaces and the Cauchy Convergence Criterion 1.4 Open and Closed Sets 1.5 Operators 1.6 The Banach Fixed-Point Theorem and the Iteration Method 1.7 Applications to Integral Equations 1.8 Applications to Ordinary Differential Equations 1.9 Continuity 1.10 Convexity 1.11 Compactness 1.12 Finite-Dimensional Banach Spaces and Equivalent Norms 1.13 The Minkowski Functional and Homeomorphisms 1.14 The Brouwer Fixed-Point Theorem 1.15 The Schauder Fixed-Point Theorem 1.16 Applications to Integral Equations 1.17 Applications to Ordinary Differential Equations 1.18 The Leray-Schauder Principle and a priori Estimates 1.19 Sub-and Supersolutions, and the Iteration Method in Ordered Banach Spaces 1.20 Linear Operators 1.21 The Dual Space 1.22 Infinite Series in Normed Spaces 1.23 Banach Algebras and Operator Functions 1.24 Applications to Linear Differential Equations in Banach Spaces 1.25 Applications to the Spectrum 1.26 Density and Approximation 1.27 Summary of Important Notions 2 Hilbert Spaces, Orthogonality, and the Dirichlet Principle 2.1 Hilbert Spaces 2.2 Standard Examples 2.3 Bilinear Forms 2.4 The Main Theorem on Quadratic Variational Problems 2.5 The Functional Analytic Justification of the Dirichlet Principle 2.6 The Convergence of the Ritz Method for Quadratic Variational Problems 2.7 Applications to Boundary-Value Problems, the Method of Finite Elements, and Elasticity 2.8 Generalized Functions and Linear Functionals 2.9 Orthogonal Projection 2.10 Linear Functionals and the Riesz Theorem 2.11 The Duality Map 2.12 Duality for Quadratic Variational Problems 2.13 The Linear Orthogonality Principle 2.14 Nonlinear Monotone Operators 2.15 Applications to the Nonlinear Lax-Milgram Theorem and the Nonlinear Orthogonality Principle 3 Hilbert Spaces and Generalized Fo\"