TRENCH_DE_STUDENT_MANUAL

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1、STUDENTSOLUTIONSMANUALFORELEMENTARYDIFFERENTIALEQUATIONSANDELEMENTARYDIFFERENTIALEQUATIONSWITHBOUNDARYVALUEPROBLEMSWilliamF.TrenchAndrewG.CowlesDistinguishedProfessorEmeritusDepartmentofMathematicsTrinityUniversitySanAntonio,Texas,USAwtrench@trinity.edu©2013WilliamF.Trench,allrightsreservedThis

2、bookwaspublishedpreviouslybyBrooks/ColeThomsonLearningReproductionispermittedforanyvalidnoncommercialeducational,mathematical,orscientificpurpose.However,chargesforprofitbeyondreasonableprintingcostsareprohibited.CORRECTIONSAREWELCOMETOBEVERLYContentsChapter1Introduction11.2FirstOrderEquations1Ch

3、apter2FirstOrderEquations52.1LinearFirstOrderEquations52.2SeparableEquations82.3ExistenceandUniquenessofSolutionsofNonlinearEquations112.4TransformationofNonlinearEquationsintoSeparableEquations132.5ExactEquations172.6IntegratingFactors21Chapter3NumericalMethods253.1Euler’sMethod253.2TheImprove

4、dEulerMethodandRelatedMethods29iiContents3.3TheRunge-KuttaMethod34Chapter4ApplicationsofFirstOrderEquations394.1GrowthandDecay394.2CoolingandMixing404.3ElementaryMechanics434.4AutonomousSecondOrderEquations454.5ApplicationstoCurves46Chapter5LinearSecondOrderEquations515.1HomogeneousLinearEquati

5、ons515.2ConstantCoefficientHomogeneousEquations555.3NonhomgeneousLinearEquations585.4TheMethodofUndeterminedCoefficientsI605.5TheMethodofUndeterminedCoefficientsII645.6ReductionofOrder755.7VariationofParameters79Chapter6ApplcationsofLinearSecondOrderEquations856.1SpringProblemsI856.2SpringProblems

6、II876.3TheRLCCircuit896.4MotionUnderaCentralForce90Chapter7SeriesSolutionsofLinearSecondOrderEquations1087.1ReviewofPowerSeries917.2SeriesSolutionsNearanOrdinaryPointI937.3SeriesSolutionsNearanOrdinaryPointII967.4RegularSingularPoints;EulerEquations1027.5TheMethodofFrobeniusI1037.6TheMethodofFr

7、obeniusII1087.7TheMethodofFrobeniusIII118Chapter8LaplaceTransforms1258.1IntroductiontotheLaplaceTransform1258.2TheInverseLaplaceTransform1278.3SolutionofInitialValueProblems1348.4TheUnitStepFunction1408.5ConstantCoefficientEquation