現代數學物理方法（第1捲） 下載 mobi epub pdf 電子書 2025

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內容簡介

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.

目錄

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

現代數學物理方法（第1捲） 下載 mobi epub pdf txt 電子書 格式

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上課要用。還好，內容豐富，可以當字典用。

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活動時買的，書的作者是大傢，讀過之後有很大收獲。活動時買的，書的作者是大傢，讀過之後有很大收獲。活動時買的，書的作者是大傢，讀過之後有很大收獲。

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泛函經典之作，印刷還好

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對學習研究專業領域有價值

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值得一讀的參考書

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數學物理以研究物理問題為目標的數學理論和數學方法。它探討物理現象的數學模型，即尋求物理現象的數學描述，並對模型已確立的物理問題研究其數學解法，然後根據解答來詮釋和預見物理現象，或者根據物理事實來修正原有模型。“數學物理”，是數學和物理學的交叉領域，指應用特定的數學方法來研究物理學的某些部分。對應的數學方法也叫數學物理方法。包括微分方程、作用量理論等多方麵。

評分☆☆☆☆☆

物超所值，沒有見過這麼便宜的貨瞭！

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