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首页 [数学]高等数学方法.pdf

[数学]高等数学方法.pdf

[数学]高等数学方法.pdf

上传者: chen_47964 2013-05-12 评分 5 0 171 23 779 暂无简介 简介 举报

简介:本文档为《[数学]高等数学方法pdf》,可适用于自然科学领域,主题内容包含IntroductiontoMethodsofAppliedMathematicsorAdvancedMathematicalMethodsforS符等。

IntroductiontoMethodsofAppliedMathematicsorAdvancedMathematicalMethodsforScientistsandEngineersSeanMauchhttp:wwwitscaltecheduseanJanuary,ContentsAntiCopyrightxvPrefacexviiAdvicetoTeachersxviiAcknowledgmentsxviiWarningsandDisclaimersxviiSuggestedUsexviiiAbouttheTitlexviiiIAlgebraSetsandFunctionsSetsSingleValuedFunctionsInversesandMultiValuedFunctionsTransformingEquationsExercisesHintsSolutionsVectorsVectorsScalarsandVectorsTheKroneckerDeltaandEinsteinSummationConventionTheDotandCrossProductSetsofVectorsinnDimensionsExercisesHintsSolutionsIICalculusDifferentialCalculusLimitsofFunctionsContinuousFunctionsTheDerivativeImplicitDifferentiationMaximaandMinimaMeanValueTheoremsApplication:UsingTaylor’sTheoremtoApproximateFunctionsApplication:FiniteDifferenceSchemesiL’Hospital’sRuleExercisesLimitsofFunctionsContinuousFunctionsTheDerivativeImplicitDifferentiationMaximaandMinimaMeanValueTheoremsL’Hospital’sRuleHintsSolutionsQuizQuizSolutionsIntegralCalculusTheIndefiniteIntegralTheDefiniteIntegralDefinitionPropertiesTheFundamentalTheoremofIntegralCalculusTechniquesofIntegrationPartialFractionsImproperIntegralsExercisesTheIndefiniteIntegralTheDefiniteIntegralTheFundamentalTheoremofIntegrationTechniquesofIntegrationImproperIntegralsHintsSolutionsQuizQuizSolutionsVectorCalculusVectorFunctionsGradient,DivergenceandCurlExercisesHintsSolutionsQuizQuizSolutionsIIIFunctionsofaComplexVariableComplexNumbersComplexNumbersTheComplexPlanePolarFormArithmeticandVectorsIntegerExponentsRationalExponentsExercisesiiHintsSolutionsFunctionsofaComplexVariableCurvesandRegionsThePointatInfinityandtheStereographicProjectionAGentleIntroductiontoBranchPointsCartesianandModulusArgumentFormGraphingFunctionsofaComplexVariableTrigonometricFunctionsInverseTrigonometricFunctionsRiemannSurfacesBranchPointsExercisesHintsSolutionsAnalyticFunctionsComplexDerivativesCauchyRiemannEquationsHarmonicFunctionsSingularitiesCategorizationofSingularitiesIsolatedandNonIsolatedSingularitiesApplication:PotentialFlowExercisesHintsSolutionsAnalyticContinuationAnalyticContinuationAnalyticContinuationofSumsAnalyticFunctionsDefinedinTermsofRealVariablesPolarCoordinatesAnalyticFunctionsDefinedinTermsofTheirRealorImaginaryPartsExercisesHintsSolutionsContourIntegrationandtheCauchyGoursatTheoremLineIntegralsContourIntegralsMaximumModulusIntegralBoundTheCauchyGoursatTheoremContourDeformationMorera’sTheoremIndefiniteIntegralsFundamentalTheoremofCalculusviaPrimitivesLineIntegralsandPrimitivesContourIntegralsFundamentalTheoremofCalculusviaComplexCalculusExercisesHintsSolutionsiiiCauchy’sIntegralFormulaCauchy’sIntegralFormulaTheArgumentTheoremRouche’sTheoremExercisesHintsSolutionsSeriesandConvergenceSeriesofConstantsDefinitionsSpecialSeriesConvergenceTestsUniformConvergenceTestsforUniformConvergenceUniformConvergenceandContinuousFunctionsUniformlyConvergentPowerSeriesIntegrationandDifferentiationofPowerSeriesTaylorSeriesNewton’sBinomialFormulaLaurentSeriesExercisesSeriesofConstantsUniformConvergenceUniformlyConvergentPowerSeriesIntegrationandDifferentiationofPowerSeriesTaylorSeriesLaurentSeriesHintsSolutionsTheResidueTheoremTheResidueTheoremCauchyPrincipalValueforRealIntegralsTheCauchyPrincipalValueCauchyPrincipalValueforContourIntegralsIntegralsontheRealAxisFourierIntegralsFourierCosineandSineIntegralsContourIntegrationandBranchCutsExploitingSymmetryWedgeContoursBoxContoursDefiniteIntegralsInvolvingSineandCosineInfiniteSumsExercisesHintsSolutionsivIVOrdinaryDifferentialEquationsFirstOrderDifferentialEquationsNotationExampleProblemsGrowthandDecayOneParameterFamiliesofFunctionsIntegrableFormsSeparableEquationsExactEquationsHomogeneousCoefficientEquationsTheFirstOrder,LinearDifferentialEquationHomogeneousEquationsInhomogeneousEquationsVariationofParametersInitialConditionsPiecewiseContinuousCoefficientsandInhomogeneitiesWellPosedProblemsEquationsintheComplexPlaneOrdinaryPointsRegularSingularPointsIrregularSingularPointsThePointatInfinityAdditionalExercisesHintsSolutionsQuizQuizSolutionsFirstOrderLinearSystemsofDifferentialEquationsIntroductionUsingEigenvaluesandEigenvectorstofindHomogeneousSolutionsMatricesandJordanCanonicalFormUsingtheMatrixExponentialExercisesHintsSolutions

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