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1、.NotesonDifferentialEquationsRobertE.TerrellPrefaceThesenotesaremostlyfromlecturesIhavegiventostudentsofscienceandengineering,whileteachingtheEngineeringMathematicscoursesatCornellUniversity.Thenotescouldbeusedforanintroductoryunifiedcourseonordinaryandpartialdifferentialequations.However,thisisnot
2、atextbookintheusualsense,andcertainlynotareference.Thestressisonclarity,notcompleteness.Itisanintroductionandaninvitation.Mostideasaretaughtbyexample.Thenoteshavebeenavailableformanyyearsfrommywebpage.Forfullercoverage,seeanyoftheexcellentbooks:•Agnew,RalphPalmer,DifferentialEquations,McGraw–Hill
3、,1960•Churchill,RuelV.,FourierSeriesandBoundaryValueProblems,Mc-GrawHill,1941•Hubbard,JohnH.,andWest,BeverlyH.,DifferentialEquations,aDynamicalSystemsApproach,Parts1and2,Springer,1995and1996•Lax,P.,andTerrell,M.,CalculusWithApplications,Springer,2014•Seeley,RobertT.,AnIntroductiontoFourierSeriesa
4、ndIntegrals,W.A.Benjamin,1966Someoftheexerciseshavetheformat“What’srongwiththis?”.Theseareeitherquestionsaskedbystudentsorerrorstakenfromtestpapersofstudentsinthisclass,soitcouldbequitebeneficialtostudythem.RobertE.TerrellJanuary1997September2005April2009March2014iContents1IntroductiontoOrdinaryD
5、ifferentialEquations11.1TheBanker’sEquation......................11.2SlopeFields............................22AGalleryofDifferentialEquations53IntroductiontoPartialDifferentialEquations73.1AConservationLaw.......................83.2TravelingWaves.........................94TheLogisticPopulationModel
6、125SeparableEquations146SeparablePartialDifferentialEquations177ExistenceandUniquenessandSoftware217.1TheExistenceTheorem.....................217.2Software..............................238LinearFirstOrderEquations258.1Newton’sLawofCooling....................268.2Investments.......................
7、.....289[oiler’s]Euler’sNumericalMethod3010SecondOrderLinearEquations3510.1Linearity..............................3510.2TheCharacteristicEquation...................3610.3Conservationlaws,part2....................38ii11TheHea
