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首页 Mathematica7.0

Mathematica7.0.pdf

Mathematica7.0

peaceraku
2013-11-30 0人阅读 举报 0 0 暂无简介

简介:本文档为《Mathematica7.0pdf》,可适用于IT/计算机领域

MathematicaDemystifiedDemystifiedSeriesAccountingDemystifiedAdvancedCalculusDemystifiedAdvancedPhysicsDemystifiedAdvancedStatisticsDemystifiedAlgebraDemystifiedAlternativeEnergyDemystifiedAnatomyDemystifiedAstronomyDemystifiedAudioDemystifiedBiochemistryDemystifiedBiologyDemystifiedBiotechnologyDemystifiedBusinessCalculusDemystifiedBusinessMathDemystifiedCDemystifiedCalculusDemystifiedChemistryDemystifiedCircuitAnalysisDemystifiedCollegeAlgebraDemystifiedCommoditiesDemystifiedComplexVariablesDemystifiedCorporateFinanceDemystifiedDatabasesDemystifiedDiabetesDemystifiedDifferentialEquationsDemystifiedDigitalElectronicsDemystifiedDiscreteMathematicsDemystifiedDosageCalculationsDemystifiedEarthScienceDemystifiedElectricityDemystifiedElectronicsDemystifiedEnvironmentalScienceDemystifiedEverydayMathDemystifiedFertilityDemystifiedFinancialPlanningDemystifiedForensicsDemystifiedFrenchDemystifiedGeneticsDemystifiedGeometryDemystifiedGermanDemystifiedGlobalWarmingandClimateChangeDemystifiedHedgeFundsDemystifiedInvestingDemystifiedItalianDemystifiedJapaneseDemystifiedJavaDemystifiedJavaScriptDemystifiedLatinDemystifiedLeanSixSigmaDemystifiedLinearAlgebraDemystifiedMacroeconomicsDemystifiedManagementAccountingDemystifiedMathematicaDemystifiedMathProofsDemystifiedMathWordProblemsDemystifiedMATLABR©DemystifiedMedicalBillingandCodingDemystifiedMedicalChartingDemystifiedMedicalSurgicalNursingDemystifiedMedicalTerminologyDemystifiedMeteorologyDemystifiedMicrobiologyDemystifiedMicroeconomicsDemystifiedNanotechnologyDemystifiedNurseManagementDemystifiedOOPDemystifiedOptionsDemystifiedOrganicChemistryDemystifiedPharmacologyDemystifiedPhysicsDemystifiedPhysiologyDemystifiedPreAlgebraDemystifiedPrecalculusDemystifiedProbabilityDemystifiedProjectManagementDemystifiedPsychologyDemystifiedQuantumFieldTheoryDemystifiedQuantumMechanicsDemystifiedRealEstateMathDemystifiedRelativityDemystifiedRoboticsDemystifiedSalesManagementDemystifiedSignalsandSystemsDemystifiedSixSigmaDemystifiedSpanishDemystifiedSQLDemystifiedStatisticsDemystifiedStringTheoryDemystifiedTechnicalAnalysisDemystifiedTechnicalMathDemystifiedTrigonometryDemystifiedVitaminsandMineralsDemystifiedMathematicaDemystifiedJimHosteNewYorkChicagoSanFranciscoLisbonLondonMadridMexicoCityMilanNewDelhiSanJuanSeoulSingaporeSydneyTorontoCopyright©byTheMcGrawHillCompanies,IncAllrightsreservedExceptaspermittedundertheUnitedStatesCopyrightActof,nopartofthispublicationmaybereproducedordistributedinanyformorbyanymeans,orstoredinadatabaseorretrievalsystem,withoutthepriorwrittenpermissionofthepublisherISBN:MHID:ThematerialinthiseBookalsoappearsintheprintversionofthistitle:ISBN:,MHID:AlltrademarksaretrademarksoftheirrespectiveownersRatherthanputatrademarksymbolaftereveryoccurrenceofatrademarkedname,weusenamesinaneditorialfashiononly,andtothebenefitofthetrademarkowner,withnointentionofinfringementofthetrademarkWheresuchdesignationsappearinthisbook,theyhavebeenprintedwithinitialcapsMcGrawHilleBooksareavailableatspecialquantitydiscountstouseaspremiumsandsalespromotions,orforuseincorporatetrainingprogramsTocontactarepresentativepleasevisittheContactUspageatwwwmhprofessionalcomInformationcontainedinthisworkhasbeenobtainedbyTheMcGrawHillCompanies,Inc(“McGrawHill”)fromsourcesbelievedtobereliableHowever,neitherMcGrawHillnoritsauthorsguaranteetheaccuracyorcompletenessofanyinformationpublishedherein,andneitherMcGrawHillnoritsauthorsshallberesponsibleforanyerrors,omissions,ordamagesarisingoutofuseofthisinformationThisworkispublishedwiththeunderstandingthatMcGrawHillanditsauthorsaresupplyinginformationbutarenotattemptingtorenderengineeringorotherprofessionalservicesIfsuchservicesarerequired,theassistanceofanappropriateprofessionalshouldbesoughtTERMSOFUSEThisisacopyrightedworkandTheMcGrawHillCompanies,Inc(“McGrawHill”)anditslicensorsreserveallrightsinandtotheworkUseofthisworkissubjecttothesetermsExceptaspermittedundertheCopyrightActofandtherighttostoreandretrieveonecopyofthework,youmaynotdecompile,disassemble,reverseengineer,reproduce,modify,createderivativeworksbasedupon,transmit,distribute,disseminate,sell,publishorsublicensetheworkoranypartofitwithoutMcGrawHill’spriorcosentYoumayusetheworkforyourownnoncommercialandpersonaluseanyotheruseoftheworkisstrictlyprohibitedYourrighttousetheworkmaybeterminatedifyoufailtocomplywiththesetermsTHEWORKISPROVIDED“ASIS”McGRAWHILLANDITSLICENSORSMAKENOGUARANTEESORWARRANTIESASTOTHEACCURACY,ADEQUACYORCOMPLETENESSOFORRESULTSTOBEOBTAINEDFROMUSINGTHEWORK,INCLUDINGANYINFORMATIONTHATCANBEACCESSEDTHROUGHTHEWORKVIAHYPERLINKOROTHERWISE,ANDEXPRESSLYDISCLAIMANYWARRANTY,EXPRESSORIMPLIED,INCLUDINGBUTNOTLIMITEDTOIMPLIEDWARRANTIESOFMERCHANTABILITYORFITNESSFORAPARTICULARPURPOSEMcGrawHillanditslicensorsdonotwarrantorguaranteethatthefunctionscontainedintheworkwillmeetyourrequirementsorthatitsoperationwillbeuninterruptedorerrorfreeNeitherMcGrawHillnoritslicensorsshallbeliabletoyouoranyoneelseforanyinaccuracy,errororomission,regardlessofcause,intheworkorforanydamagesresultingtherefromMcGrawHillhasnoresponsibilityforthecontentofanyinformationaccessedthroughtheworkUndernocircumstancesshallMcGrawHillandoritslicensorsbeliableforanyindirect,incidental,special,punitive,consequentialorsimilardamagesthatresultfromtheuseoforinabilitytousethework,evenifanyofthemhasbeenadvisedofthepossibilityofsuchdamagesThislimitationofliabilityshallapplytoanyclaimorcausewhatsoeverwhethersuchclaimorcausearisesincontract,tortorotherwiseToMary,Benjamin,andGraemeABOUTTHEAUTHORJimHoste,PhD,isamathematicsprofessoratPitzerCollegeandhasusedMathematicasinceitsinitialreleaseinHehasbeenanassociateeditoroftheJournalofKnotTheoryandItsRamificationssinceandhasauthoreddozensofresearchpublicationsCONTENTSPrefacexiiiAcknowledgmentsxviiCHAPTERGettingStartedStartingMathematicaEnteringExpressionsEditingCellsBasicArithmeticUsingPreviousResultsExactversusApproximateUsingFunctionsUsingVariablesUsingCommentsSuppressingOutputAbortingaCalculationListsPalettesSavingandPrintingOurWorkGettingHelp!FindOutMoreQuizviiiMathematicaDemystifiedCHAPTERTwoDimensionalGraphicsThePlotFunctionResizingGraphicsGraphicsOptionsDrawingToolsandtheGraphicInspectorUsingEpilogMouseoverEffectsTooltipAnimationUsingManipulatePlottingPointswithListPlotCurveFittingPlottinginPolarCoordinatesParametricPlotsDrawingShapesSavingandPrintingGraphicsFindOutMoreQuizCHAPTERGettingHelpSyntaxColoringDelimiterMatchingSettingPreferencesTheHelpMenuWritingGoodCodeMonitoringCalculationsGettingOutofTroubleAskanExpertFindOutMoreQuizCHAPTEROddsandEndsTransformingExpressionsReplacementRulesWorkingwithListsSumsandProductsContentsixMatricesFindOutMoreQuizCHAPTERFunctionsDefiningFunctionsPureFunctionsElementaryProgrammingUsingModulesFindOutMoreQuizCHAPTERThreeDimensionalGraphicsThePlotDFunctionDGraphicsOptionsSurfacesofRevolutionDrawingContoursorLevelSetsDrawingCurvesinSpaceDrawingGraphicsPrimitivesFindOutMoreQuizCHAPTERCalculusLimitsOneSidedLimitsMultivariableLimitsDerivativesMinimumMaximumProblemsSeriesIntegrationAntidifferentiationApplicationsofIntegrationFindOutMoreQuizxMathematicaDemystifiedCHAPTERSolvingEquationsPolynomialEquationsSystemsofPolynomialEquationsSystemsofLinearEquationsNonpolynomialEquationsDifferentialEquationsFindOutMoreQuizCHAPTERWorkingwithDataCountryDataWordPlayGraphsAGlimpseofOtherDataSetsFindOutMoreQuizCHAPTERDynamicalSystemsandFractalsIteratingaFunctionGraphicalAnalysisTheQuadraticFamilyJuliaSetsCustomColoringMakingMoviesTheMandelbrotSetWhatIsaFractalFindOutMoreQuizCHAPTERLookingGoodCellStylingTheOptionInspectorCellPropertiesContentsxiUsingPalettesCellGroupingHyperlinksAddingGraphicstoNotebooksCreatingSlideshowsFindOutMoreQuizFinalExamAnswersIndexThispageintentionallyleftblankPREFACE•WhatIsMathematicaMathematicaisaprogramfordoingmathematicsUsingMathematicaitiseasyto–Makenumericandsymboliccalculations–Simplifycomplicatedmathematicalexpressions–Plotthegraphsoffunctionsaswellascurvesandsurfacesinspace–Createsophisticatedcolorgraphics–Computederivativesandintegrals–Solveequations,includingdifferentialequations–Workwithlargedatasets–Createanimations–Writeprogramstocarryoutanyalgorithm–CreateslideshowpresentationsThelatestversionofMathematica,Version,ispackedwithallsortsofnewcapabilitiesincludingadynamicinterfacethatallowstheusertointeractwithgraphics,aswellasotherkindsofoutputinrealtimeThenewversionofMathematicaisalsofastManyoftheunderlyingroutineshavebeenoptimizedforgreaterspeedWhetheryouareahighschoolstudentoraPhDmathematician,physicist,orengineer,Mathematicaisanidealtoolformeetingyourcomputationalneeds•WhoIsThisBookforThisbookisintendedprimarilyforMathematicanewcomerspeoplewhohaveneverusedMathematica,orwhohaveuseditverylittleWe’lltakeyoufromyourveryfirstcalculationallthewaytoplottingbeautifulfractalsThebookincludeshundredsofexampleseachwithstepbystepexplanationsUsingthisbook,youcanprogressfromknowingnothingatallaboutxivMathematicaDemystifiedMathematicatobeingabletouseMathematicaforallofthetaskslistedaboveandmoreExperiencedMathematicauserswhohaveyettolearnallthenewfeaturesofVersionsandshouldalsofindthebookhelpfulWhileweassumeyouknownothingaboutMathematica,wedoassumethatyouknowalittlemathematics,atleasthighschoolalgebraAhighschoolstudentwhohasyettolearncalculusmayfindthechapteroncalculusabitmysterious,butthereareplentyofneatthingstolearnintheotherchaptersCollegestudentswhoarecurrentlytakingcalculus,linearalgebra,ordifferentialequationscanusethisbookasacompaniontext,anddoyourhomeworkwithMathematicaInadditiontoteachingyouMathematica,theexampleswillintroduceyoutosomebeautifulandexcitingmathematicsThebookprovidesglimpsesofsomerealmathematicalgemsincludingafewconjecturesthathavevexedmathematiciansforhundredsofyearsSo,you’llnotonlylearnMathematica,butsomeneatmathematicstoo!•What’sinThisBookMathematicaishuge,really,reallybigAnybookcancoveronlyasmallfractionofMathematicaOurgoalistocoverenoughmaterialsothatafterreadingthisbookyoucandoquiteafewthingswithMathematica,probablyasmuchasmostpeoplewouldeverwanttodoPlus,youdon’thavetoreadthewholebookIf,forexample,youmainlywanttouseMathematicatoproducegraphics,youcanskipthelaterchaptersthatdon’tdealwithgraphicsButperhapsmoreimportantthanteachingyouaspecificsetofMathematicafeatures,we’llbeteachingyouhowtousetheonlineMathematicadocumentationsothatyoucanteachyourselftogobeyondthebasicsofthisbookEachchaptercontainsasectiontitled“FindOutMore”thatwilldirectyoutoguidesandtutorialsintheMathematicaDocumentationCenterthatelaborateonthematerialinthatchapterForthemostpart,eachchapterdealswithaspecifictopicwithinMathematica,forexample,threedimensionalgraphics,orsolvingequationsTheoneexceptionisChapterthatinsteadfocusesonamathematicaltopic,inthiscase,dynamicalsystemsandfractals,andshowshowtouseMathematicatodrawbeautifulfractalsincludingJuliasetsandthefamousMandlebrotsetWithonlyoneexception,thechaptersareorderedsothateachMathematicafunctionisthoroughlyexplainedwhenitisfirstintroducedandbeforeitisusedinlaterchaptersStill,itisnotnecessarytoreadthechaptersinthegivenorderHowever,ifyouareacompletebeginner,youshouldatleastreadChaptersto(orperhapsatleastto)beforeskippingaroundYoucouldprobablyreadthechapteronthreedimensionalgraphicsrightafterthechapterontwodimensionalgraphics,especiallyifyouarewillingtoPrefacexvflipbacktoearliersectionsinthebookoccasionallytofillinsomemissingdetailsThelastchapterwillshowyouhowtoaddtextandorganizeyourMathematicaNotebookssothattheyaremorethanmerescratchsheetsforyourcalculationsIfyouareastudentwhoplanstodomathematicshomeworkwithMathematica,don’tputoffreadingthischapter!EachchaptercloseswithaQuiz,andaFinalExamcanbefoundattheendofthebookTheQuizandExamquestionsvaryfromfairlyeasytoquitechallengingTrytodothemyourselfbeforelookingattheanswers!JimHosteClaremont,CAJuly,ThispageintentionallyleftblankACKNOWLEDGMENTSAnumberofpeoplehaveofferedhelpfulcommentsandsuggestionsThanksareduetoJudithGrabinerforseveralofthehistoricalremarksinthebookRobertFierroofferedusefulfeedbackwhentheprojectwasjustbeginningPaulWellinfromWolframResearchsharedsomesamplenotebooksthatwereinspirationalJudyBass,atMcGrawHill,providedvaluableguidanceandsupportThispageintentionallyleftblankCHAPTERGettingStartedStartingMathematicaWhenwestartMathematicaafreshwindow,ornotebook,willopenThisiswherewewilldoallofourmathematicalcalculationsandgraphicsAtthetopofthewindowweseethetitleofthewindow,whichinitiallyis“untitled”Later,whenweseehowtosaveourworkasafile,wecangiveanametothefile,andthatnamewillappearinthetitlebarofthewindowEnteringExpressionsLet’sdoourfirstcalculation!IfwetypeandthenpressShiftReturn(ie,holddowntheShiftkeyandthentheReturnkey)MathematicacomputesthesumandplacestheansweronthenextlineinthewindowThisiscalledevaluatingorenteringtheexpressionThewindownowcontainsOnMackeyboards,ShiftReturnisthesameasEnterWitheitherWindowsorMacOS,usingtheReturnkeywillsimplymovethecursortothenextline,allowingustotypemoreMathematicaDemystifiedExampleIn:=Out=NoticethatMathematicahasplaced“In:=”and“Out=”labelstotheleftofand,respectivelyTotherightoftheinputandoutput,MathematicahasplacedasetofbracketsThetwoinnermostbracketsenclosetheinputandoutput,respectively,andthelargerbracketgroupstheinputandoutputtogetherEachbracketcontainswhatisknownasacellAllofthecalculationsthatwedointhisnotebookwillbeorganizedintocellsandthebracketsthatsurroundthecellswillcomeinhandyfororganizingourworkWe’llhavealotmoretosayaboutthisinChap,sodon’tworrytoomuchaboutthebracketsnowInfact,untilwegettoChapwewillbeomittingthebracketsmostofthetimewhenwedisplayMathematicainputandoutputEditingCellsLet’schangetoMathematicasupportsalltheusualmousedriventexteditingfeaturesofwordprocessorsWecansimplyusethemousetoplacethecursorintheinputcellandedittheentrysothatitreadsToredothecalculation,wenowreenterthecellbyonceagainpressingShiftReturnTheresultisExampleIn:=Out=NoticethatthetheInandOutlabelshavechangedto“In:=”and“Out=”Eachtimewereevaluateacell,thenumbersintheInandOutlabelswillchangeTocreateanewcellwithanewcalculation,simplystarttypingMathematicawillplacetheinputinanewcellWhenmanycellsarepresentwecanusethemousetoplacethecursorbetweenexistingcellsandclickthemousebuttontoinsertanewcellatthatlocationNoticehowthecursorchangesfromaverticalbarwhenlocatedinsideacell,toahorizontalbarwhenlocatedbetweencellsWiththecursorbetweencells,clickthemousebuttonandthenstarttypingMathematicawillcreateanewcellatthedesiredlocationCHAPTERGettingStartedFinally,wecanalsoclickonthebracketwhichenclosesacelltoselectitAfterselectingacellwecanreevaluateitbypressingShiftReturnortreatitjustlikeanyselectediteminatextdocumentandcut,copy,orpasteasusualTrydeletinganentirecellbyclickingonitsbracketandthenchoosingEdit�Cutfromthemenubar,(orusingtheequivalentkeyboardshortcut)Therearelotsofwaysthatwecanchangetheappearanceofcells,changingthefont,fontsize,color,andthelikeWe’llexplorethesetopicsinChapBasicArithmeticMathematicacandoallthebasicoperationsofaddition,subtraction,multiplication,division,andexponentiation(raisingonenumbertoanother)whicharedenotedbythesymbols,−,∗,,andˆWecanalsouseparenthesisforgroupingasusualHereisanexampleinvolvingthearithmeticoperationsExampleIn:=*Out=^Heretheexponentiationwasdonefirst,giving*,thenthemultiplication,whichleadsto,andfinallytheadditionMathematicafollowsthestandardorderofoperations,firstperformingallexponentiation(fromlefttoright),thenallmultiplicationsanddivisions(againfromlefttoright),andfinally,alladditionsandsubtractions(fromlefttoright)IfwewanttooverridetheseconventionsweneedtouseparenthesistogrouptermsOnenicefeatureofMathematicaisthatofimpliedmultiplicationWedonotneedtousethemultiplicationsign∗inordertomultiplyInstead,ablankspacebetweenthingsthatcanbemultiplied(numbers,variables,expressions)willbetreatedasmultiplicationTheblankspacecanevenbeomittedifparenthesisareusedtoindicatemultiplicationIfwedoleaveablankspaceformultiplication,sometimesMathematicawillfillinthespacewiththemultiplicationsymbol×Basically,wecanty

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