数学物理 [Mathematics for Physics and Physicists] 下载 mobi epub pdf 电子书 2024

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内容简介

　　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.

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目录

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

数学物理 [Mathematics for Physics and Physicists] 下载 mobi epub pdf txt 电子书 格式

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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，并针对模型已确立的物理问题研究其数学解法，此解释和预见物理现象，或者根据物理事实来修正原有模型。物理问题的研究一直和数学密切相关。在牛顿力学中，质点和刚体的运动用常微分方程来描述，求解这些方程就成为牛顿力学中的重要数学问题。18世纪以来，在连续介质力学、传热学和电磁场理论中，归结出许多偏微分方程，通称数学物理方程。20世纪初，数学物理方程的研究开始成为数学物理的主要内容。此后基于等离子体物理、固体物理、非线性光学、空间技术、核技术等方面的需要，又有许多新的偏微分方程问题出现，如孤立子波，间断解，分歧解，反问题等，它们使数学物理方程的内容进一步丰富起来。20世纪以来，由于物理学内容的更新，数学物理也有了新的面貌。伴随着对电磁理论和引力场的深入研究，人们对时空观念发生了根本的变化。这使得闵科夫斯基空间和黎曼空间的几何学成为爱因斯坦狭义相对论和广义相对论所必需的数学理论。在探讨大范围时空结构时，还需要整体微分几何。量子力学和量子场论的产生，使数学物理添加了非常丰富的内容。物理对象中揭示出的多种多样的对称性使得群论显得非常有用。晶体的结构就是由欧几里得空间运动群的若干子群给出的。正交群和洛伦兹群的各种表示对讨论具有时空对称性的许多物理问题有很重要的作用。对基本粒子相互作用的内在对称性的研究更导致了杨-米尔斯理论的产生。这个理论以规范势为出发点，而它就是数学家所研究的纤维丛上的联络。有关纤维丛的拓扑不变量也开始对物理学发挥作用。微观的物理对象往往有随机性。在经典的统计物理学中需要对各种随机过程的统计规律有深入的研究。随着电子计算机发展，数学物理里的许多问题能通过数值计算来解决。由此发展起来的计算力学、计算物理都发挥着越来越大的作用。科学的发展表明，数学物理的内容越来越丰富，解决物理问题的能力也越来越强。数学物理的研究对数学也有很大的促进作用，它是产生数学的新思想、新对象、新问题以及新方法的一个源泉。

评分☆☆☆☆☆

全是英文的，价格有点贵，不错。

评分☆☆☆☆☆

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.

评分☆☆☆☆☆

还是书的旁边有烂的地方，看着有点像盗版的啊，不过特价买的就那样了；哦

评分☆☆☆☆☆

　　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.

评分☆☆☆☆☆

帮老公买的 屯着吧 还没看

评分☆☆☆☆☆

全是英文的，价格有点贵，不错。

评分☆☆☆☆☆

赶特价，买经典。京东活动很给力

评分☆☆☆☆☆

　　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.

类似图书 点击查看全场最低价