應用泛函分析（第2捲）（英文版） [Applied Functional AnalysisMa:In Principles and Their Applications] epub pdf mobi txt 電子書 下載 2024

應用泛函分析（第2捲）（英文版） [Applied Functional AnalysisMa:In Principles and Their Applications] epub pdf mobi txt 電子書 下載 2024

☆☆☆☆☆
簡體網頁||繁體網頁



點擊這裡下載

應用泛函分析（第2捲）（英文版） [Applied Functional AnalysisMa:In Principles and Their Applications] epub pdf mobi txt 電子書 下載 2024

类似图書 點擊查看全場最低價

---

內容簡介

　　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.

內頁插圖

目錄

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.

應用泛函分析（第2捲）（英文版） [Applied Functional AnalysisMa:In Principles and Their Applications] epub pdf mobi txt 電子書 下載 2024

應用泛函分析（第2捲）（英文版） [Applied Functional AnalysisMa:In Principles and Their Applications] 下載 epub mobi pdf txt 電子書

評分☆☆☆☆☆

專業人士使用。。。。。。。。。。

評分☆☆☆☆☆

相當專業的書籍，對我幫助很大。

評分☆☆☆☆☆

微分的概念可以在巴拿赫空間中得到推廣，微分算子作用於其上的所有函數，一個函數在給定點的微分是一個連續綫性映射。

評分☆☆☆☆☆

書是好書，印刷質量一般

評分☆☆☆☆☆

質量又好送貨又快，一直信賴京東

評分☆☆☆☆☆

由於泛函分析源自研究各種函數空間，在函數空間裏函數列的收斂有不同的類型（譬如逐點收斂，一緻收斂，弱收斂等等），這說明函數空間裏有不同的拓撲。而函數空間一般是無窮維綫性空間。所以抽象的泛函分析研究的是一般的（無窮維的）帶有一定拓撲的綫性空間。

評分☆☆☆☆☆

拓撲綫性空間的定義就是一個帶有拓撲結構的綫性空間，使得綫性空間的加法和數乘都是連續映射的空間。

評分☆☆☆☆☆

內容和印刷都很好，值得購買

評分☆☆☆☆☆

拓撲綫性空間

类似图書 點擊查看全場最低價