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物理学和工程学中的计算方法（第2版）

物理学和工程学中的计算方法（第2版）
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作者: 著
出版社: 世界图书出版公司
2000-06
版次: 1
ISBN: 9787506247207
定价: 60.00
装帧: 平装
开本: 24开
纸张: 胶版纸
页数: 508页
分类: 自然科学
23人买过
  • 　　Computationalmethodsformanincreasinglyimportantpartoftheundergraduatecurricu-luminphysicsandengineeringthesedays.Thisbookismainlyconcernedwiththewaysthatcomputersmaybeusedtoadvanceastudentsunderstandingofphysics.Alargepartofthematerialiscommontoengineeringaswell.Thesubjectmattercoveredinthisvolumemaybeclassifiedalsounderthetitleof"computationalphysics."Thereareseveralwaystoorganizethematerialthatshouldbeincluded.Thechoicemadehereistofollowthetraditionalapproachofmathematicalphysics.Thatis，thechaptersandsectionsaregroupedaroundmethods，withphysicalproblemsusedasthemotivationandexamples.Oneattractivealternativeistogrouparoundphysicalphenomena.Thedifficultyoffollowingthiswayoforganizationistheheavyrelianceonthephysicsbackgroundofthereaders，thusmakingithardertofollowforstudentsatearlystagesoftheireducation.Forthisreason，suchanapproachisrejected.
    　　此书为英文版！ PrefacetotheFirstEdition
    PrefacetotheSecondEdition
    1ComputationalMethods
    1-1Numericalcalculationsandbeyond
    1-2Integersandfloatingnumbers
    1-3Programminglanguageandprogramlibrary
    1-4Examplesofalgebraic,integerandfloatingnumbercalculations
    1-5Examplesofunconventionaltechniques
    Problems
    2IntegrationandDifferentiation
    2-1Numericalintegration
    2-2Rectangularandtrapezoidalrules
    2-3Simpsonsrule
    2-4Gaussianquadrature
    2-5MonteCarlointegration
    2-6Multidimensionalintegralsandimproperintegrals
    2-7Numericaldifferentiation
    Problems
    3InterpolationandExtrapolation
    3-1Polynomialinterpolation
    3-2Interpolationusingrationalfunctions
    3-3Continuedfraction
    3-4Fouriertransform
    3-5Extrapolation
    3-6Inverseinterpolation
    3-7Cubicspline
    Problems
    4SpecialFunctions
    4-1Hermitepolynomialsandharmonicoscillator
    4-2Legendrepolynomialsandsphericalharmonics
    4-3SphericalBesselfunctions
    4-4Laguerrepolynomials
    4-5Errorintegralsandgammafunctions
    Problems
    5Matrices
    5-1Systemoflinearequations
    5-2MatrixinversionandLU-decomposition
    5-3Matrixapproachtotheeigenvalueproblem
    5-4Tridiagonalizationmethod
    5-5Eigenvaluesandeigenvectorsofatridiagonalmatrix
    5-6Lanczosmethodofconstructingmatrices
    5-7Nonsymmetricmatricesandcomplexmatrices
    Problems
    6MethodsofLeastSquares
    6-1Statisticaldescriptionofdata
    6-2Uncertaintiesandtheirpropagation
    6-3Themethodofmaximumlikelihood
    6-4Themethodofleastsquares
    6-5Statisticaltestsoftheresults
    6-6Linearleast-squaresfit
    6-7Nonlinearleast-squaresfittodata
    Problems
    7MonteCarloCalculations
    7-1Generationofrandomnumbers
    7-2MoleculardiffusionandBrownianmotion
    7-3Datasimulationandhypothesistesting
    7-4Percolationandcriticalphenomena
    7-5TheIsingmodel
    7-6Pathintegralsinquantummechanics
    7-7Fractals
    Problems
    8FiniteDifferenceSolutionofDifferentialEquations
    8-1Typesofdifferentialequations
    8-2Runge-Kuttamethods
    8-3Solutionofinitialvalueproblemsbyextrapolation
    8-4Boundaryvalueproblemsbyshootingmethods
    8-5Relaxationmethods
    8-6Boundaryvalueproblemsinpartialdifferentialequations
    8-7Parabolicpartialdifferentialequations
    8-8Hyperbolicpartialdifferentialequations
    8-9Nonlineardifferentialequations
    8-10Stiffnessproblems
    Problems
    9FiniteElementSolutiontoPDE
    9-1Background
    9-2Shapefunctionsandfiniteelementapproximation
    9-3Assemblingcontributionsfromelements
    9-4Variationalapproach
    9-5Applicationtoatwo-dimensionalPoissonequation
    Problems
    AppendixA
    A-1Decompositionintoprimenumbers
    A-2Bit-reversedorder
    A-3Gaussianeliminationofatridiagonalmatrix
    A-4Randombitgenerator
    A-5Reductionofhigher-orderODEtofirst-order
    AppendixBListofFortranProgramExamples
    Bibliography
    Index
  • 内容简介:
    　　Computationalmethodsformanincreasinglyimportantpartoftheundergraduatecurricu-luminphysicsandengineeringthesedays.Thisbookismainlyconcernedwiththewaysthatcomputersmaybeusedtoadvanceastudentsunderstandingofphysics.Alargepartofthematerialiscommontoengineeringaswell.Thesubjectmattercoveredinthisvolumemaybeclassifiedalsounderthetitleof"computationalphysics."Thereareseveralwaystoorganizethematerialthatshouldbeincluded.Thechoicemadehereistofollowthetraditionalapproachofmathematicalphysics.Thatis，thechaptersandsectionsaregroupedaroundmethods，withphysicalproblemsusedasthemotivationandexamples.Oneattractivealternativeistogrouparoundphysicalphenomena.Thedifficultyoffollowingthiswayoforganizationistheheavyrelianceonthephysicsbackgroundofthereaders，thusmakingithardertofollowforstudentsatearlystagesoftheireducation.Forthisreason，suchanapproachisrejected.
    　　此书为英文版！
  • 目录:
    PrefacetotheFirstEdition
    PrefacetotheSecondEdition
    1ComputationalMethods
    1-1Numericalcalculationsandbeyond
    1-2Integersandfloatingnumbers
    1-3Programminglanguageandprogramlibrary
    1-4Examplesofalgebraic,integerandfloatingnumbercalculations
    1-5Examplesofunconventionaltechniques
    Problems
    2IntegrationandDifferentiation
    2-1Numericalintegration
    2-2Rectangularandtrapezoidalrules
    2-3Simpsonsrule
    2-4Gaussianquadrature
    2-5MonteCarlointegration
    2-6Multidimensionalintegralsandimproperintegrals
    2-7Numericaldifferentiation
    Problems
    3InterpolationandExtrapolation
    3-1Polynomialinterpolation
    3-2Interpolationusingrationalfunctions
    3-3Continuedfraction
    3-4Fouriertransform
    3-5Extrapolation
    3-6Inverseinterpolation
    3-7Cubicspline
    Problems
    4SpecialFunctions
    4-1Hermitepolynomialsandharmonicoscillator
    4-2Legendrepolynomialsandsphericalharmonics
    4-3SphericalBesselfunctions
    4-4Laguerrepolynomials
    4-5Errorintegralsandgammafunctions
    Problems
    5Matrices
    5-1Systemoflinearequations
    5-2MatrixinversionandLU-decomposition
    5-3Matrixapproachtotheeigenvalueproblem
    5-4Tridiagonalizationmethod
    5-5Eigenvaluesandeigenvectorsofatridiagonalmatrix
    5-6Lanczosmethodofconstructingmatrices
    5-7Nonsymmetricmatricesandcomplexmatrices
    Problems
    6MethodsofLeastSquares
    6-1Statisticaldescriptionofdata
    6-2Uncertaintiesandtheirpropagation
    6-3Themethodofmaximumlikelihood
    6-4Themethodofleastsquares
    6-5Statisticaltestsoftheresults
    6-6Linearleast-squaresfit
    6-7Nonlinearleast-squaresfittodata
    Problems
    7MonteCarloCalculations
    7-1Generationofrandomnumbers
    7-2MoleculardiffusionandBrownianmotion
    7-3Datasimulationandhypothesistesting
    7-4Percolationandcriticalphenomena
    7-5TheIsingmodel
    7-6Pathintegralsinquantummechanics
    7-7Fractals
    Problems
    8FiniteDifferenceSolutionofDifferentialEquations
    8-1Typesofdifferentialequations
    8-2Runge-Kuttamethods
    8-3Solutionofinitialvalueproblemsbyextrapolation
    8-4Boundaryvalueproblemsbyshootingmethods
    8-5Relaxationmethods
    8-6Boundaryvalueproblemsinpartialdifferentialequations
    8-7Parabolicpartialdifferentialequations
    8-8Hyperbolicpartialdifferentialequations
    8-9Nonlineardifferentialequations
    8-10Stiffnessproblems
    Problems
    9FiniteElementSolutiontoPDE
    9-1Background
    9-2Shapefunctionsandfiniteelementapproximation
    9-3Assemblingcontributionsfromelements
    9-4Variationalapproach
    9-5Applicationtoatwo-dimensionalPoissonequation
    Problems
    AppendixA
    A-1Decompositionintoprimenumbers
    A-2Bit-reversedorder
    A-3Gaussianeliminationofatridiagonalmatrix
    A-4Randombitgenerator
    A-5Reductionofhigher-orderODEtofirst-order
    AppendixBListofFortranProgramExamples
    Bibliography
    Index
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