应用泛函分析（第2卷）（英文版） [Applied Functional AnalysisMa:In Principles and Their Applications] epub pdf mobi txt 电子书 下载 2024

应用泛函分析（第2卷）（英文版） [Applied Functional AnalysisMa:In Principles and Their Applications] epub pdf mobi txt 电子书 下载 2024

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应用泛函分析（第2卷）（英文版） [Applied Functional AnalysisMa:In Principles and Their Applications] epub pdf mobi txt 电子书 下载 2024

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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.

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目录

Preface
Contents of AMS Volume 108
1　The Hahn-Banach Theorem Optimization Problems
1.1 The Hahn-Banach Theorem
1.2 Applications to the Separation of Convex Sets
1.3 The Dual Space C[a, b]*
1.4 Applications to the Moment Problem
1.5 Minimum Norm Problems and Duality Theory
1.6 Applications to Cebysev Approximation
1.7 Applications to the Optimal Control of Rockets
2 Variational Principles and Weak Convergence
2.1 The nth Variation
2.2 Necessary and Sufficient Conditions for Local Extrema and the Classical Calculus of Variations
2.3 The Lack of Compactness in Infinite-Dimensional Banach Spaces
2.4 Weak Convergence
2.5 The Generalized Weierstrass Existence Theorem
2.6 Applications to the Calculus of Variations
2.7 Applications to Nonlinear Eigenvalue Problems
2.8 Reflexive Banach Spaces
2.9 Applications to Convex Minimum Problems and Variational Inequalities
2.10 Applications to Obstacle Problems in Elasticity
2.11 Saddle Points
2.12 Applications to Dui~lity Theory
2.13 The von Neumann Minimax Theorem on the Existence of Saddle Points
2.14 Applications to Game Theory
2.15 The Ekeland Principle about Quasi-Minimal Points
2.16 Applications to a General Minimum Principle via the Palais-Smale Condition
2.17 Applications to the Mountain Pass Theorem
2.18 The Galerkin Menhod and Nonlinear Monotone Operators
2.19 Symmetries and Conservation Laws (The Noether Theorem
2.20 The Basic Ideas of Gauge Field Theory
2.21 Representations of Lie Algebras
2.22 Applications to Elementary Particles
3 Principles of Linear Functional Analysis
3.1 The Baire Theorem
3.2 Application to the Existence of Nondifferentiable Continuous Functions
3.3 The Uniform Boundedness Theorem
3.4 Applications to Cubature Formulas
3.5 The Open Mapping Theorem
3.6 Product Spaces
3.7 The Closed Graph Theorem
3.8 Applications to Factor Spaces
3.9 Applications to Direct Sums and Projections
3.10 Dual Operators
3.11 The Exactness of the Duality Functor
3.12 Applications to the Closed Range Theorem and to Fredholm Alternatives
4 The Implicit Function Theorem
4.1 m-Linear Bounded Operators
4.2 The Differential of Operators and the Fr~chet Derivative
4.3 Applications to Analytic Operators
4.4 Integration
4.5 Applications to the Taylor Theorem
4.6 Iterated Derivatives
4.7 The Chain Rule
4.8 The Implicit Function Theorem
4.9 Applications to Differential Equations
4.10 Diffeomorphisms and the Local Inverse Mapping Theorem
4.11 Equivalent Maps and the Linearization Principle
4.12 The Local Normal Form for Nonlinear Double Splitting Maps
4.13 The Surjective Implicit Function Theorem
4.14 Applications to the Lagrange Multiplier Rule
5 Fredholm Operators
5.1 Duality for Linear Compact Operators
5.2 The Riesz-Schauder Theory on Hilbert Spaces
5.3 Applications to Integral Equations
5.4 Linear Fredholm Operators
5.5 The Riesz-Schauder Theory on Banach Spaces
5.6 Applications to the Spectrum of Linear Compact Operators
5.7 The Parametrix
5.8 Applications to the Perturbation of Fredholm Operators
5.9 Applications to the Product Index Theorem
5.10 Fredholm Alternatives via Dual Pairs
5.11 Applications to Integral Equations and Boundary-Value Problems
5.12 Bifurcation Theory
5.13 Applications to Nonlinear Integral Equations
5.14 Applications to Nonlinear Boundary-Value Problems
5.15 Nonlinear Fredholm Operators
5.16 Interpolation Inequalities
5.17 Applications to the Navier-Stokes Equations References
List of Symbols
List of Theorems
List of Most Important Definitions
Subject Index

前言/序言

　　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.

应用泛函分析（第2卷）（英文版） [Applied Functional AnalysisMa:In Principles and Their Applications] epub pdf mobi txt 电子书 下载 2024

应用泛函分析（第2卷）（英文版） [Applied Functional AnalysisMa:In Principles and Their Applications] 下载 epub mobi pdf txt 电子书 2024

评分☆☆☆☆☆

微分的概念可以在巴拿赫空间中得到推广，微分算子作用于其上的所有函数，一个函数在给定点的微分是一个连续线性映射。

评分☆☆☆☆☆

作者是泛函分析的大家，还写了一套非线性泛函分析，值得买！

评分☆☆☆☆☆

很好的书啊。很好的

评分☆☆☆☆☆

经典的书，没啥好评论的，印刷质量高点就好了

评分☆☆☆☆☆

一本泛函分析的经典教材，感觉是看过的类似的书中最好的一本了。

评分☆☆☆☆☆

这是最常见，应用最广的一类拓扑线性空间。比如有限闭区间上的连续函数空间，有限闭区间上的k次可微函数空间。或者对于每个实数p，如果p ≥ 1，一个巴拿赫空间的例子是“所有绝对值的p次方的积分收敛的勒贝格可测函数”所构成的空间。（参看Lp空间）

评分☆☆☆☆☆

在别处买了第一卷，凑全

评分☆☆☆☆☆

一直在京东买书，今天下单明天就到，直接送货上门，特别方便，价格也比实体店要优惠很多，而且书都是正版的，质量很不错，给京东点赞。

评分☆☆☆☆☆

质量又好送货又快，一直信赖京东

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