现代数学物理方法（第1卷） epub pdf mobi txt 电子书 下载 2024

现代数学物理方法（第1卷） epub pdf mobi txt 电子书 下载 2024

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现代数学物理方法（第1卷） epub pdf mobi txt 电子书 下载 2024

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内容简介

This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modem mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modem physics, and partial differenrial equations.

目录

Preface
Introduction
Contents of Other Volumes
I: PRELIMINARIES
1. Sets and functions
2. Metric and normed linear spaces
Appendix Lira sup and lim inf
3. The Lebesgue integral
4. Abstract measure theory
5. Two conrergence arguments
6. Equicontinuity
Notes
Problems

II: HILBERT SPACES
1. The geometry of Hilbert space
2. The Riesz lemma
3. Orthonormal bases
4. Tensor products of Hilbert spaces
5. Ergodic theory: an introduction
Notes
Problems

III: BANACH SPACES
1. Definition and examples
2. Duals and double duals
3. The Hahn-Banach theorem
4. Operations on Banach spaces
5. The Baire category theorem and its consequences
Notes
Problems
IV: TOPOLOGICAL SPACES
1. General notions
2. Nets and Convergence
3. Compactness
Appendix The Stone-Weierstrass theorem
4. Measure theory on Compact spaces
5. Weak topologies on Banach spaces
Appendix Weak and strong measurability
Notes
Problems


V: LOCALLY ONVEX SPACES
1. General properties
2. Frdchet spaces
3. Functions of rapid decease and the tempered distributions
Appendix The N-representation for and
4. Inductive limits: generalized functions and weak solutions of partial differential equations
5. Fixed point theorems
6. Applications of fixed point theorems
7. Topologies on locally convex spaces: duality theory and the strong dual topology
Appendix Polars and the Mackey-Arens theorem
Notes
Problems
VI: BOUNDED OPERATORS
VII: THE SPECTRAL THEOREM
VIII: UNBOUNDED OPERATORS
THE FOURIER TRANSFORM
SUPPLEMENTARY MATERIAL
List of Symbols

前言/序言

现代数学物理方法（第1卷） epub pdf mobi txt 电子书 下载 2024

现代数学物理方法（第1卷） 下载 epub mobi pdf txt 电子书 2024

评分☆☆☆☆☆

专业人士使用。。。。。。。。。。

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值得一读的参考书

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非常好的书，快递给力

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物理用泛函，这个形容差不多吧，个人看法，勿撕。

评分☆☆☆☆☆

非常好的书！

评分☆☆☆☆☆

数学味比较浓。讲的比国内课本多很多。

评分☆☆☆☆☆

数学物理以研究物理问题为目标的数学理论和数学方法。它探讨物理现象的数学模型，即寻求物理现象的数学描述，并对模型已确立的物理问题研究其数学解法，然后根据解答来诠释和预见物理现象，或者根据物理事实来修正原有模型。“数学物理”，是数学和物理学的交叉领域，指应用特定的数学方法来研究物理学的某些部分。对应的数学方法也叫数学物理方法。包括微分方程、作用量理论等多方面。

评分☆☆☆☆☆

很经典的一本教材，好好学一下

评分☆☆☆☆☆

很好的教材，适合研究生和专业研究人员阅读。

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