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| 作者 |
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DennisG.Zill
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| ISBN |
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7506272431
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| 页数 |
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859
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| 封面形式 |
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简裝本
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| 出版社 |
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世界图书出版公司
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| 出版日期 |
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2004-11-1
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| NT$ |
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694
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配送说明： 国际快递 ， 海运邮递 。
付款说明： 1. VISA、MASTER線上刷卡 2. 信用卡传真刷卡付款 3.
邮政划拨 4. 银行汇款
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Inrecentyears,partiallyduetoevolvingtechnologyanditsexpandingimportanceinpedagogyandtothereformmovementincalculus,changeshaveoccurredinthecoursecalled"DifferentialEquations."Instructorsarequestioningaspectsofboththetraditionalteachingmethodsusedandthetraditionalcontentofthecourse.Thishealthyintrospectionisimportantinmakingthesubjectmatternotonlymoreinterestingforstudentsbutalsomorerelevanttotheworldinwhichtheylive.
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PREFACEix
ACKNOWLEDGMENTSxv
1INTRODUCTIONTODIFFERENTIALEQUATIONS1
1.1DefinitionsandTerminology2
1.2Initial-ValueProblems15
1.3DifferentialEquationsasMathematicalModels22
Chapter1inReview37
2FIRST-ORDERDIFFERENTIALEQUATIONS39
2.1SolutionCurvesWithouttheSolution40
2.2SeparableVariables51
2.3LinearEquations60
2.4ExactEquations72
2.5SolutionsbySubstitutions80
2.6ANumericalSolution86
Chapter2inReview92
3MODELINGWITHFIRST-ORDERDIFFERENTIALEQUATIONS95
3.1LinearEquations96
3.2NonlinearEquations109
3.3SystemsofLinearandNonlinearDifferentialEquations121
Chapter3inReview130
ProjectModule:HarvestingofRenewableNaturalResources,byGilbertN.Lewis133
4HIGHER-ORDERDIFFERENTIALEQUATIONS138
4.1PreliminaryTheory:LinearEquations139
4.1.1Initial-ValueandBoundary-ValueProblems139
4.1.2HomogeneousEquations142
4.1.3NonhomogeneousEquations148
4.2ReductionofOrder154
4.3HomogeneousLinearEquationswithConstantCoefficients158
4.4UndeterminedCoefficients--SuperpositionApproach167
4.5UndeterminedCoefficients--AnnihilatorApproach178
4.6VariationofParameters188
4.7Cauchy-EulerEquation193
4.8SolvingSystemsofLinearEquationsbyElimination201
4.9NonlinearEquations207
Chapter4inReview212
5MODELINGWITHHIGHER-ORDERDIFFERENTIALEQUATIONS215
5.1LinearEquations:Initial-ValueProblems216
5.1.1Spring/MassSystems:FreeUndampedMotion216
5.1.2Spring/MassSystems:FreeDampedMotion220
5.1.3Spring/MassSystems:DrivenMotion224
5.1.4SeriesCircuitAnalogue227
5.2LinearEquations:Boundary-ValueProblems237
5.3NonlinearEquations247
Chapter5inReview259
ProjectModule:TheCollapseoftheTacomaNarrowsSuspensionBridge,byGilbertN.Lewis263
6SERIESSOLUTIONSOfLINEAREQUATIONS267
6.1SolutionsAboutOrdinaryPoints268
6.1.1ReviewofPowerSeries268
6.1.2PowerSeriesSolutions271
6.2SolutionsAboutSingularPoints280
6.3TwoSpecialEquations292
Chapter6inReview304
7THELAPLACETRANSFORM306
7.1DefinitionoftheLaplaceTransform307
7.2InverseTransformandTransformsofDerivatives314
7.3TranslationTheorems324
7.3.1Translationonthes-Axis324
7.3.2Translationonthet-Axis328
7.4AdditionalOperationalProperties338
7.5DiracDeltaFunction351
7.6SystemsofLinearEquations354
Chapter7inReview361
8SYSTEMSOFLINEARFIRST-ORDERDIFFERENTIALEQUATIONS364
8.1PreliminaryTheory365
8.2HomogeneousLinearSystemswithConstantCoefficients375
8.2.1DistinctRealEigenvalues376
8.2.2RepeatedEigenvalues380
8.2.3ComplexEigenvalues384
8.3VariationofParameters393
8.4MatrixExponential399
Chapter8inReview404
ProjectModule:EarthquakeShakingofMultistoryBuildings,byGilbertN.Lewis406
9NUMERICALSOLUTIONSOFORDINARYDIFFERENTIALEQUATIONS410
9.1EulerMethodsandErrorAnalysis411
9.2Runge-KuttaMothods417
9.3MultistepMethods424
9.4Higher-OrderEquationsandSystems427
9.5Second-OrderBoundary-ValueProblems433
Chapter9inReview438
APPENDIXESAPP-1
IOammaFunctionsAPP-1
IIIntroductiontoMatricesAPP-3
IIILaplaceTransformsAPP-25
SELECTEDANSWERSFORODD-NUMBEREDPROBLEMSAN-1
INDEXI-1
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