微分方程与边界值问题（英文版第5版）

图书标准信息

• 作者 兹尔 著
• 出版社 机械工业出版社
• 出版时间 2003-06
• 版次 1
• ISBN 9787111123187
• 定价 69.00元
• 装帧 平装
• 开本 其他
• 纸张 胶版纸
• 页数 631页
• 丛书 经典原版书库

【内容简介】

　　微分方程问题是工程和应用数学领域的重要问题。本书是作者多年教学经验的总结，示例丰富、内容全面。条理清晰。在编写的过程中，作者一直遵循便于学生理解和记忆的原则，所以本书的内容没有采用过于理论化的方式，而是以直观、易读的方式表述。本书对传统的教学方式和教学内容的各个方面都进行了革新，不仅内容更加吸引读者，同时加强了与现实世界的联系，使传统的教学内容与新知识完美结合。

【目录】

PREFACEIX
ACKNOWLEDGMENTSXIIi
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，by
GilbertN.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:TheCollapseoftheTacomaNarrows
SuspensionBridge，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，by
GilbertN.Lewis406
9NUMERICALSOLUTIONSOfORDINARYDIFFERENTIALEQUATIONS410
9.1EulerMethodsandErrorAnalysis411
9.2Runge-KuttaMethods417
9.3MultistepMethods424
9.4Higher-OrderEquationsandSystems427
9.5Second-OrderBoundary-ValueProblems433
Capter9inReview438
10PLANEAUTONOMOUSSYSTEMSANDSTABILITY439
10.1AutonomousSystems，CriticalPoints，andPeriodicSolutions440
10.2StabilityofLinearSystems448
10.3LinearizationandLocalStability458
10.4ModelingUsingAutonomousSystems470
Chapter10inReview480
11ORTHOGONALFUNCTIONSANDFOURIERSERIES483
11.1OrthogonalFunctions484
11.2FourierSeries489
11.3FourierCosineandSineSeries495
11.4Sturm-LiouvilleProblem504
11.5BesselandLegendreSeries511
11.5.1Fourier-BesselSeries512
11.5.2Fourier-LegendreSeries515
Chapter11inReview519
PARTIALDIFFERENTIALEQUATIONSAND
12BOUNDARY-VALUEPROBLEMSINRECTANGULARCOORDINATES521
12.1SeparablePartialDifferentialEquations522
12.2ClassicalEquationsandBoundary-ValueProblems527
12.3HeatEquation533
12.4WaveEquation536
12.5LaplacesEquation542
12.6NonhomogeneousEquationsandBoundaryConditions547
12.7OrthogonalSeriesExpansions551
12.8Boundary-ValueProblemsInvolvingFourierSeriesinTwo
Variables555
Chapter12inReview559
13BOUNDARY-VALUEPROBLEMSINOTHERCOORDINATESYSTEMS561
13.1ProblemsInvolvingLaplacesEquationinPolarCoordinates562
13.2ProblemsinPolarandCylindricalCoordinates:Bessel
Functions567
13.3ProblemsinSphericalCoordinates:LegendrePolynomials575
Chapter13inReview578
14INTEGRALTRANSFORMMETHOD581
14.1ErrorFunction582
14.2ApplicationsoftheLaplaceTransform584
14.3FourierIntegral595
14.4FourierTransforms601
Chapter14inReview607
15NUMERICALSOLUTIONSOFPARTIALDIFFERENTIALEQUATIONS610
15.1EllipticEquations611
15.2ParabolicEquations617
15.3HyperbolicEquations625
Chapter15inReview630
APPENDIXESAPP-1
IGammaFunctionAPP-1
IIIntroductiontoMatricesAPP-3
IIILaplaceTransformsAPP-25
SELECTEDANSWERSFORODD-NUMBERED
PROBLEMSAN-1
INDEXI-1