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內容簡介

　　There is a fairly fasbionable current of thought that bolds that the use of advanced mathematics is of little real use in physics， and goes sometimes as far as to say that knowing convinced that matbematics is stikll a parecious source of insight， not for students of physics， but also for researchers.
　　Many only see mathematics as a tool-and of course， it is part a tool， but they should be reminded that， as Galileo said， the book of Nature is written in give examples that knowing mathematics provides the means to understand precise physical notions， to use them more easily， to establish them on a sure foundation， and even more importantly， to discover new ones.

內頁插圖

目錄

A book's apoLogy
Index of notation

1 Reminders： convergence of sequences and series
1.1 The problem of limits in physics
1.1.a Two paradoxes involving kinetic energy
1.1.b Romeo, Juliet, and viscous fluids
1.1.c Potential wall in quantum mechanics
1.1.d Semi-infinite filter behaving as waveguide
1.2 Sequences
1.2.a Sequences in a normed vector space
1.2.b Cauchy sequences
1.2.c The fixed point theorem
1.2.d Double sequences
1.2.e Sequential definition of the limit of a function
1.2.f Sequences of functions
1.3 Series
1.3.a Series in a normed vector space
1.3.b Doubly infinite series
1.3.c Convergence of a double series
1.3.d Conditionally convergent series, absolutely convergent series
1.3.e Series of functions
1.4 Power series, analytic functions
1.4.a Taylor formulas
1.4.b Some numerical illustrations
1.4.c Radius of convergence of a power series
1.4.d Analytic functions
1.5 A quick look at asymptotic and divergent series
1.5.a Asymptotic series
1.5.b Divergent series and asymptotic expansions
Exercises
Problem
Solutions

2 Measure theary and the Lebesgue integral
2.1 The integral according to Mr. Riemann
2.1.a Riemann sums
2.1.b Limitations of Riemann's definition
2.2 The integral according to Mr. Lebesgue
2.2.a Principle of the method
2.2.b Borel subsets
2.2.c Lebesgue measure
2.2.d The Lebesgue -algebra
2.2.e Negligible sets
2.2.f Lebesgue measure on Rn
2.2.g Definition ofthe Lebesgue integral
2.2.h Functions zero almost everywhere, space L1
2.2.1 And today?
Exercises
Solutions

3 Integral calculus
3.1 Integrability in practice
3.1.a Standard functions
3.l.b Comparison theorems
3.2 Exchanging integrals and limits or series
3.3 Integrals with parameters
3.3.a Continuity of functions defined by integrals
3.3.b Differentiating under the integral sign
3.3.c Case of parameters appearing in the integration range
3.4 Double and multiple integrals
3.5 Change of variables
Exercises
Solutions

4 Complex Analysis Ⅰ
4.1 Holomorphic functions
4.1.a Definitions
4.2 Cauchy's theorem
4.3 Properties of holomorphic functions
4.4 Singularities of a function
4.5 Laurent series
……
5 Complex Analysis Ⅱ
6 Conformal maps
7 Distributions Ⅰ
8 Distributions II
9 Hilbert spaces, Fourier series
10 Fourier transform of functions
11 Fourier transform of distributions
12 The Laplace transform
13 Physical applications of the Fourier transform
14 Bras, kets, and all that sort of thing
15 Green functions
16 Tensors
17 Differential forms
18 Groups and group representations
19 Introduction to probability theory
20 Random variables
21 Convergence of random variables： central limit theorem
Appendices
Tables

前言/序言

數學物理 [Mathematics for Physics and Physicists] 下載 mobi epub pdf txt 電子書

評分☆☆☆☆☆

　　Many only see mathematics as a tool-and of course， it is part a tool， but they should be reminded that， as Galileo said， the book of Nature is written in give examples that knowing mathematics provides the means to understand precise physical notions， to use them more easily， to establish them on a sure foundation， and even more importantly， to discover new ones.

評分☆☆☆☆☆

‘內容全麵’，‘講解詳細’……這本書買傢印象比較多，應該是一本銷量比較多的書~~

評分☆☆☆☆☆

There is a fairly fasbionable current of thought that bolds that the use of advanced mathematics is of little real use in physics， and goes sometimes as far as to say that knowing convinced that matbematics is stikll a parecious source of insight， not for students of physics， but also for researchers.

評分☆☆☆☆☆

　　Many only see mathematics as a tool-and of course， it is part a tool， but they should be reminded that， as Galileo said， the book of Nature is written in give examples that knowing mathematics provides the means to understand precise physical notions， to use them more easily， to establish them on a sure foundation， and even more importantly， to discover new ones.

評分☆☆☆☆☆

　　Many only see mathematics as a tool-and of course， it is part a tool， but they should be reminded that， as Galileo said， the book of Nature is written in give examples that knowing mathematics provides the means to understand precise physical notions， to use them more easily， to establish them on a sure foundation， and even more importantly， to discover new ones.

評分☆☆☆☆☆

全是英文的，價格有點貴，不錯。

評分☆☆☆☆☆

　　Many only see mathematics as a tool-and of course， it is part a tool， but they should be reminded that， as Galileo said， the book of Nature is written in give examples that knowing mathematics provides the means to understand precise physical notions， to use them more easily， to establish them on a sure foundation， and even more importantly， to discover new ones.

評分☆☆☆☆☆

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，並針對模型已確立的物理問題研究其數學解法，此解釋和預見物理現象，或者根據物理事實來修正原有模型。物理問題的研究一直和數學密切相關。在牛頓力學中，質點和剛體的運動用常微分方程來描述，求解這些方程就成為牛頓力學中的重要數學問題。18世紀以來，在連續介質力學、傳熱學和電磁場理論中，歸結齣許多偏微分方程，通稱數學物理方程。20世紀初，數學物理方程的研究開始成為數學物理的主要內容。此後基於等離子體物理、固體物理、非綫性光學、空間技術、核技術等方麵的需要，又有許多新的偏微分方程問題齣現，如孤立子波，間斷解，分歧解，反問題等，它們使數學物理方程的內容進一步豐富起來。20世紀以來，由於物理學內容的更新，數學物理也有瞭新的麵貌。伴隨著對電磁理論和引力場的深入研究，人們對時空觀念發生瞭根本的變化。這使得閔科夫斯基空間和黎曼空間的幾何學成為愛因斯坦狹義相對論和廣義相對論所必需的數學理論。在探討大範圍時空結構時，還需要整體微分幾何。量子力學和量子場論的産生，使數學物理添加瞭非常豐富的內容。物理對象中揭示齣的多種多樣的對稱性使得群論顯得非常有用。晶體的結構就是由歐幾裏得空間運動群的若乾子群給齣的。正交群和洛倫茲群的各種錶示對討論具有時空對稱性的許多物理問題有很重要的作用。對基本粒子相互作用的內在對稱性的研究更導緻瞭楊-米爾斯理論的産生。這個理論以規範勢為齣發點，而它就是數學傢所研究的縴維叢上的聯絡。有關縴維叢的拓撲不變量也開始對物理學發揮作用。微觀的物理對象往往有隨機性。在經典的統計物理學中需要對各種隨機過程的統計規律有深入的研究。隨著電子計算機發展，數學物理裏的許多問題能通過數值計算來解決。由此發展起來的計算力學、計算物理都發揮著越來越大的作用。科學的發展錶明，數學物理的內容越來越豐富，解決物理問題的能力也越來越強。數學物理的研究對數學也有很大的促進作用，它是産生數學的新思想、新對象、新問題以及新方法的一個源泉。

評分☆☆☆☆☆

‘內容全麵’，‘講解詳細’……這本書買傢印象比較多，應該是一本銷量比較多的書~~

類似圖書 點擊查看全場最低價