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物理學家用的數學方法-第7版

包郵 物理學家用的數學方法-第7版

作者:阿夫肯
出版社:世界圖書出版公司出版時間:2014-03-01
開本: 16開 頁數: 1205
本類榜單:自然科學銷量榜
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物理學家用的數學方法-第7版 版權信息

物理學家用的數學方法-第7版 本書特色

阿夫肯著的《物理學家用的數學方法(第7版)(精)》是為具有研究生水平的讀者編寫的一部入門性工具書,語言簡練,結構流暢,可讀性很強,很受讀者歡迎,本書是第7版。本版全面介紹了物理學中常用數學方法,內容涉及物理學中用到的數學內容,包括矢量/張量分析,矩陣,群論,數列與復變函數,各種特殊函數,微分方程,傅里葉分析與積分變換,非線性方法,變分法和概率論等諸多領域,是從事物理學研究和教學人員的案頭**書。 讀者對象:物理、數學及相關專業的研究生和科教工作者。

物理學家用的數學方法-第7版 內容簡介

阿夫肯著的《物理學家用的數學方法(第7版)(精)》是為具有研究生水平的讀者編寫的一部入門性工具書,語言簡練,結構流暢,可讀性很強,很受讀者歡迎,本書是第7版。本版全面介紹了物理學中常用數學方法,內容涉及物理學中用到的數學內容,包括矢量/張量分析,矩陣,群論,數列與復變函數,各種特殊函數,微分方程,傅里葉分析與積分變換,非線性方法,變分法和概率論等諸多領域,是從事物理學研究和教學人員的案頭**書。 讀者對象:物理、數學及相關專業的研究生和科教工作者。

物理學家用的數學方法-第7版 目錄

preface
1 mathematical preliminaries
 1.1 infiniteseries
 1.2 series offunctions
 1.3 binomial theorem
 1.4 mathematical induction
 1.5 operations on series expansions of functions
 1.6 some important series
 1.7 vectors
 1.8 complex numbers and functions
 1.9 derivatives andextrema
 1.10 evaluation oflntegrals
 1.1 i dirac delta function
 additionaireadings
2 determinants and matrices
 2.1 determinants
 2.2 matrices
 additionai readings
3 vector analysis
 3.1 review ofbasic properties
 3.2 vectors in 3-d space 
 3.3 coordinate transformations
 3.4 rotations in ir3
 3.5 differential vector operators
 3.6 differential vector operators: further properties
 3.7 vectorlntegration
 3.8 integral theorems
 3.9 potentiaitheory
 3.10 curvilinear coordinates
 additionaireadings
4 tensors and differential forms
 4.1 tensoranalysis
 4.2 pseudotensors, dual tensors
 4.3 tensors in general coordinates
 4.4 jacobians
 4.5 differentialforms
 4.6 differentiatingforms
 4.7 integratingforms
 additionalreadings
5 vector spaces
 5.1 vectors in function spaces
 5.2 gram-schmidt orthogonalization
 5.3 operators
 5.4 selfadjointoperators
 5.5 unitaty operators
 5.6 transformations of operators
 5.7 invariants
 5.8 summary-vector space notation
 additionaireadings
6 eigenvalue problems
 6.1 eigenvalueequations
 6.2 matrix eigenvalue problems
 6.3 hermitian eigenvalue problems
 6.4 hermitian matrix diagonalization
 6.5 normaimatrices
 additionalreadings
7 ordinary difterential equations
 7.1 introduction
 7.2 first-orderequations
 7.3 odes with constant coefficients
 7.4 second-order linear odes
 7.5 series solutions-frobenius ' method
 7.6 othersolutions
 7.7 inhomogeneous linear odes
 7.8 nonlinear differential equations
 additional readings
8 sturm-liouville theory
 8.1 introduction
 8.2 hermitian operators
 8.3 ode eigenvalue problems
 8.4 variation method
 8.5 summary, eigenvalue problems
 additional readings
9 partial differential equations
 9.1 introduction
 9.2 first-order equations
 9.3 second-order equations
 9.4 separation of variables
 9.5 laplace and poisson equations
 9.6 wave equation
 9.7 heat-flow, or diffusion pde
 9.8 summary
 additional readings
10 green's functions
 10.1 one-dimensional problems
 10.2 problems in two and three dimensions
 additional readings
11 complex variable theory
 11.1 complex variables and functions
 11.2 cauchy-riemann conditions
 11.3 cauchy' s integral theorem
 11.4 cauchy' s integral formula
 11.5 laurent expansion
 11.6 singularities
 11.7 calculus of residues
 11.8 evaluation of definite integrals
 11.9 evaluation of sums
 11.10 miscellaneous topics
 additional readings 
12 further topics in analysis
 12.1 orthogonal polynomials
 12.2 bernoulli numbers
 12.3 euler-maclaurin integration formula
 12.4 dirichlet series
 12.5 infinite products
 12.6 asymptotic series
 12.7 method of steepest descents
 12.8 dispersion relations
 additional readings
13 gamma function
 13.1 definitions, properties
 13.2 digamma and polygamma functions
 13.3 the beta function
 13.4 stirling's series
 13.5 riemann zeta function
 13.6 other related functions
 additional readings
14 bessel functions
 14.1 bessel functions of the first kind, ,iv (x)
 14.2 orthogonality
 14.3 neumann functions, bessel functions of the second kind
 14.4 hankel functions
 14.5 modified bessel functions, iv (x) and kv (x)
 14.6 asymptotic expansions
 14.7 spherical bessel functions
 additional readings
15 legendre functions
 15.1 legendre polynomials
 15.2 orthogonality
 15.3 physical interpretation of generating function
 15.4 associated legendre equation
 15.5 spherical harmonics
 15.6 legendre functions of the second kind
 additional readings
16 angular momentum
 16.1 angular momentum operators
 16.2 angular momentum coupling
 16.3 spherical tensors
 16.4 vector spherical harmonics
 additional readings 
17 group theory
 17.1 introduction to group theory
 17.2 representation of groups
 17.3 symmetry and physics
 17.4 discrete groups
 17.5 direct products
 17.6 symmetric group
 17.7 continuous groups
 17.8 lorentz group
 17.9 lorentz covariance of maxwell's equations
 17.10 space groups
 additional readings
18 more special functions
 18.1 hermite functions
 18.2 applications of hermite functions
 18.3 laguerre functions
 18.4 chebyshev polynomials
 18.5 hypergeometric functions
 18.6 confluent hypergeometric functions
 18.7 dilogarithm
 18.8 elliptic integrals
 additional readings
19 fourier series
 19.1 general properties
 19.2 applications of fourier series
 19.3 gibbs phenomenon 
 additional readings
20 integral transforms
 20.1 introduction
 20.2 fourier transform
 20.3 properties of fourier transforms
 20.4 fourier convolution theorem
 20.5 signal-processing applications
 20.6 discrete fourier transform
 20.7 laplace transforms
 20.8 properties of laplace transforms
 20.9 laplace convolution theorem
 20.10 inverse laplace transform
 additional readings
21 integral equations
 21.1 introduction
 21.2 some special methods
 21.3 neumann series
 21.4 hilbert-schmidt theory
 additional readings
 17.4 discrete groups
 17.5 direct products
 17.6 symmetric group
 17.7 continuous groups
 17.8 lorentz group
 17.9 lorentz covariance of maxwell's equations
 17.10 space groups
 additional readings
18 more special functions
 18.1 hermite functions
 18.2 applications of hermite functions
 18.3 laguerre functions
 18.4 chebyshev polynomials
 18.5 hypergeometric functions
 18.6 confluent hypergeometric functions
 18.7 dilogarithm
 18.8 elliptic integrals
 additional readings
19 fourier series
 19.1 general properties
 19.2 applications of fourier series
 19.3 gibbs phenomenon 
 additional readings
20 integral transforms
 20.1 introduction
 20.2 fourier transform
 20.3 properties of fourier transforms
 20.4 fourier convolution theorem
 20.5 signal-processing applications
 20.6 discrete fourier transform
 20.7 laplace transforms
 20.8 properties of laplace transforms
 20.9 laplace convolution theorem
 20.10 inverse laplace transform
 additional readings
21 integral equations
 21.1 introduction
 21.2 some special methods
 21.3 neumann series
 21.4 hilbert-schmidt theory
 additional readings
22 calculus of variations
 22.1 euler equation
 22.2 more general variations
 22.3 constrained minima/maxima
 22.4 variation with constraints 
 additional readings
23 probability and statistics
 23.1 probability: definitions, simple properties 
 23.2 random variables
 23.3 binomial distribution
 23.4 poisson distribution
 23.5 gauss' normal distribution
 23.6 transformations of random variables 
 23.7 statistics
 additional readings
index
展開全部

物理學家用的數學方法-第7版 作者簡介

Arfken, Weber, Harris是國際知名學者,在數學和物理學界享有盛譽。本書凝聚了作者多年科研和教學成果,適用于科研工作者、高校教師和研究生。

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