Mathematica by Example 5 Edition PDF
Preview Mathematica by Example 5 Edition
Mathematica by Example Mathematica by Example Fifth Edition Martha L. Abell Georgia Southern University, Statesboro, USA James P. Braselton Georgia Southern University, Statesboro, USA AcademicPressisanimprintofElsevier 125LondonWall,LondonEC2Y5AS,UnitedKingdom 525BStreet,Suite1800,SanDiego,CA92101-4495,UnitedStates 50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UnitedKingdom Copyright©2017ElsevierInc.Allrightsreserved. Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans,electronicormechanical, includingphotocopying,recording,oranyinformationstorageandretrievalsystem,withoutpermissioninwritingfromthe publisher.Detailsonhowtoseekpermission,furtherinformationaboutthePublisher’spermissionspoliciesandour arrangementswithorganizationssuchastheCopyrightClearanceCenterandtheCopyrightLicensingAgency,canbe foundatourwebsite:www.elsevier.com/permissions. ThisbookandtheindividualcontributionscontainedinitareprotectedundercopyrightbythePublisher(otherthanasmay benotedherein). Notices Knowledgeandbestpracticeinthisfieldareconstantlychanging.Asnewresearchandexperiencebroadenour understanding,changesinresearchmethods,professionalpractices,ormedicaltreatmentmaybecomenecessary. Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgeinevaluatingandusingany information,methods,compounds,orexperimentsdescribedherein.Inusingsuchinformationormethodstheyshouldbe mindfuloftheirownsafetyandthesafetyofothers,includingpartiesforwhomtheyhaveaprofessionalresponsibility. Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors,assumeanyliabilityforany injuryand/ordamagetopersonsorpropertyasamatterofproductsliability,negligenceorotherwise,orfromanyuseor operationofanymethods,products,instructions,orideascontainedinthematerialherein. LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary ISBN:978-0-12-812481-9 ForinformationonallAcademicPresspublications visitourwebsiteathttps://www.elsevier.com/books-and-journals Publisher:KateyBirtcher AcquisitionEditor:GrahamNisbet EditorialProjectManager:SusanIkeda ProductionProjectManager:PaulPrasadChandramohan Designer:MarkRogers TypesetbyVTeX Preface MathematicabyExamplebridgesthegapthatexistsbetweentheveryelementaryhandbooks availableon Mathematicaand those reference books written for the advanced Mathematica users.MathematicabyExampleisanappropriatereferenceforallusersofMathematicaand, in particular, for beginning users like students, instructors, engineers, business people, and other professionals first learning to use Mathematica. Mathematica by Example introduces theverybasiccommandsandincludestypicalexamplesofapplicationsofthesecommands. In addition, the text also includes commands useful in areas such as calculus, linear alge- bra, business mathematics, ordinary and partial differential equations, and graphics. In all cases,however,examplesfollowtheintroductionofnewcommands.Readersfromthemost elementarytoadvancedlevelswillfindthattherangeoftopicscoveredaddressestheirneeds. TakingadvantageofVersion11ofMathematica,MathematicabyExample,FifthEdition, introduces the fundamental concepts of Mathematica to solve typical problems of interest tostudents,instructors,andscientists.TheFifthEditionisanextensiverevisionofthetext. FeaturesthatmakeMathematicabyExample,FifthEdition,aseasytouseasareferenceand asusefulaspossibleforthebeginnerincludethefollowing. 1. Version 11 Compatibility. All examples illustrated in Mathematica by Example, Fifth Edition,werecompletedusingVersion11ofMathematica.Althoughmanycomputations cancontinuetobecarriedoutwithearlierversionsofMathematica,wehavetakenadvan- tageofthenewfeaturesinVersion11asmuchaspossible. 2. Applications. New applications, many of which are documented by references, from a varietyoffields,especiallybiology,physics,andengineering,areincludedthroughoutthe text.EspeciallynoticethenewexamplesregardingseriesinChapter3andmanipulation ofphotographsinChapters2,4,and5. 3. DetailedTableofContents.Thetableofcontentsincludesallchapter,section,andsub- sectionheadings.Alongwiththecomprehensiveindex,wehopethatuserswillbeableto locateinformationquicklyandeasily. 4. Additionalexamples.WehaveconsiderablyexpandedthetopicsinChapters1through6. Theresultsshouldbemoreusefultoinstructors,students,businesspeople,engineers,and otherprofessionalsusingMathematicaonavarietyofplatforms. 5. ComprehensiveIndex.Intheindex,mathematicalexamplesandapplicationsarelisted by topic, or name, as well as commands along with frequently used options: particular mathematicalexamplesaswellasexamplesillustratinghowtousefrequentlyusedcom- mands are easy to locate. In addition, commands in the index are cross-referenced with frequentlyusedoptions.Functionsavailableinthevariouspackagesarecross-referenced bothbypackageandalphabetically. 6. As technology has changed, so has the publication of a book. When Mathematica by Example was first published in 1992, it was published as a single color book. Conse- quently,atthattime,itwasimportanttousevariousgraylevelsinplotstohelpdistinguish them. Now, many of you will download an electronic copy of the text and print it on a high-resolution color printer with high-quality paper. The result will be outstanding. To illustratetheuseofcolor,wehavechosenfromvariousuniversitiesandcollegesthrough- out the United States. We tried to use the colors from at least one university or college ineachstate.Sometimesthiswasdifficulttodobecauseobtainingthecolorcodesfrom somecollegeswaseasierthanfromothers.Ofcourse,intheprintversionofthetext,all imageswillstillbeinvariouslevelsofgray. ix x Preface WebeganMathematicabyExamplein1990andthefirsteditionwaspublishedin1991. Backthen,wewereontopoftheworldusingMacintoshIIcx’swith8megsofRAMand40 megharddrives.Wetriedtochooseexamplesthatwethoughtwouldberelevanttobeginning users–typicallyinthecontextofmathematicsencounteredintheundergraduatecurriculum. ThoseexamplescouldalsobecarriedoutbyMathematicainatimelymanneronacomputer aspowerfulasaMacintoshIIcx. WhenworkingontheFifthedition,weareonthetopoftheworldwithiMacswithdual Intelprocessorscompletewith8gigsofRAMand1or2Terabyteharddrives.Nowweare working with machines with more memory than we can comprehend and so fast we can’t believethatcomputerswillbefasterbuttheywillalmostcertainlybenearlyobsoletebythe timeyouarereadingthis.TheexamplespresentedinMathematicabyExamplecontinuetobe theonesthatwethinkaremostsimilartotheproblemsencounteredbybeginningusersand arepresentedinthecontextofsomeonefamiliarwithmathematicstypicallyencounteredby undergraduates. However, for this Fifth edition of Mathematica by Example we have taken theopportunitytoexpandonseveralofourfavoriteexamplesbecausethemachinesnowhave thespeedandpowertoexplorethemingreaterdetail. OtherimprovementstotheFiftheditioninclude: 1. InChapter3,wehaveincreasedthenumberofexamplesrelatingtoapplicationsofseries, particularlydiscussing“howisπ approximatedaccuratelynow?” 2. Chapter4,IntroductiontoListsandTables,containsseveralexamplesillustratingvarious techniquesofhowtoquicklycreateplotsofbifurcationdiagrams,Juliasets,andtheMan- delbrotsetwithnewMathematicafunctionsthatmakevisualizingthesesetsremarkably easy. 3. InChapter6,wehavetakenadvantageoftheManipulatefunctiontoillustrateavariety of situations and expand on many examples throughout the chapter. For example, see Example6.13foracomparisonofsolutionsofnonlinearequationstotheircorresponding linearapproximations. 4. We have included references that we find particularly interesting in the Bibliogra- phy, even if they are not specific Mathematica-related texts. A comprehensive list of Mathematica-relatedpublicationscanbefoundattheWolframwebsite. http://store.wolfram.com/catalog/books/ Also,besuretoinvestigate,use,andsupportWolfram’sMathWorld–simplyanamazing webresourceformathematics,Mathematica,andotherinformation. http://store.wolfram.com/catalog/books/ MarthaL.Abell JamesP.Braselton Statesboro,GA,USA June,2017 Chapter 1 Getting Started 1.1 INTRODUCTION TO MATHEMATICA Mathematica,firstreleasedin1988byWolframResearch,Inc., http://www.wolfram.com/, is a system for doing mathematicson a computer.Mathematicacombinessymbolicmanip- ulation,numericalmathematics,outstandinggraphics,andasophisticatedprogramminglan- guage.Becauseofitsversatility,Mathematicahasestablisheditselfasthecomputeralgebra system of choice for many computer users. Among the over 1,000,000 users of Mathemat- ica, 28% are engineers, 21% are computer scientists, 20% are physical scientists, 12% are mathematical scientists, and 12% are business, social, and life scientists. Two-thirds of the usersareinindustryandgovernmentwithasmall(8%)butgrowingnumberofstudentusers. However, due to its special nature and sophistication, beginning users need to be aware of thespecialsyntaxrequiredtomakeMathematicaperforminthewayintended.Youwillfind thatcalculationsandsequencesofcalculationsmostfrequentlyusedbybeginningusersare discussedindetailalongwithmanytypicalexamples.Inaddition,thecomprehensiveindex not only lists a variety of topics but also cross-references commands with frequently used options. Mathematica By Example serves as a valuable tool and reference to the beginning userofMathematicaaswellastothemoresophisticateduser,withspecializedneeds. Forinformation,includingpurchasinginformation,aboutMathematicacontact: CorporateHeadquarters: WolframResearch,Inc. 100TradeCenterDrive Champaign,IL61820 USA telephone:217-398-0700 fax:217-398-0747 email:[email protected] web:http://www.wolfram.com Europe: WolframResearchEuropeLtd. 10BlenheimOfficePark LowerRoad,LongHanborough OxfordshireOX88LN UnitedKingdom telephone:+44-(0)1993-883400 fax:+44-(0)1993-883800 email:[email protected] Asia: WolframResearchAsiaLtd. IzumiBuilding8F 3-2-15Misaki-cho Chiyoda-ku,Tokyo101 Japan MathematicabyExample.http://dx.doi.org/10.1016/B978-0-12-812481-9.00001-6 Copyright©2017ElsevierInc.Allrightsreserved. 1 2 MathematicabyExample telephone:+81-(0)3-5276-0506 fax:+81-(0)3-5276-0509 email:[email protected] ANoteRegardingDifferentVersionsofMathematica WiththereleaseofVersion10.4ofMathematica,manynewfunctionsandfeatureshavebeen addedtoMathematica.WeencourageusersofearlierversionsofMathematicatoupdateto Version11assoonastheycan.AllexamplesinMathematicaByExample,fifthedition,were completedwithVersion11.Inmostcases,thesameresultswillbeobtainedifyouareusing Version10.4orlater,althoughtheappearanceofyourresultswillalmostcertainlydifferfrom thatpresentedhere.However,particularfeaturesofVersion10.4areusedandinthosecases, of course, these features are not available in earlier versions. If you are using an earlier or laterversionofMathematica,yourresultsmaynotappearinaformidenticaltothosefound in this book: some commands found in Version 11 are not available in earlier versions of Mathematica; in later versions some commands will certainly be changed, new commands added,andobsoletecommandsremoved.Fordetailsregardingthesechanges,pleasereferto the Documentation Center. You can determine the version of Mathematica you are using during a given Mathematica session by entering either the command $Versionor the com- mand$VersionNumber.Inthistext,weassumethatMathematicahasbeencorrectlyinstalled onthecomputeryouareusing.IfyouneedtoinstallMathematicaonyourcomputer,please refertothedocumentationthatcamewiththeMathematicasoftwarepackage. On-linehelpforupgradingolderversionsofMathematicaandinstallingnewversionsof MathematicaisavailableattheWolframResearch,Inc.website: http://www.wolfram.com/. DetailsregardingwhatisdifferentinMathematica11frompreviousversionsofMathe- maticacanbefoundat http://www.wolfram.com/mathematica/new-in-11/?source=frontpage-stripe. GettingStarted Chapter | 1 3 Also,whenyougototheWolframDocumentationcenter(underHelpintheMathematica menu) you can choose Wolfram Documentation to see the major differences. Also, the upperright handcorner of the mainhelp pagefor eachfunctionwilltell youif it is new in Version11orhasbeenupdatedinVersion11. 1.1.1 Getting Started with Mathematica We begin by introducing the essentials of Mathematica. The examples presented are taken fromalgebra,trigonometry,andcalculustopicsthatmostreadersarefamiliarwithtoassist youinbecomingacquaintedwiththeMathematicacomputeralgebrasystem. WeassumethatMathematicahasbeencorrectlyinstalledonthecomputeryouareusing. IfyouneedtoinstallMathematicaonyourcomputer,pleaserefertothedocumentationthat camewiththeMathematicasoftwarepackage. Start Mathematica on your computer system. Using Windows or Macintosh mouse or keyboardcommands,starttheMathematicaprogrambyselectingtheMathematicaiconoran existing Mathematica document (or notebook), and then clicking, double-clicking or right- clickingandselectingOpenontheicon. IfyoustartMathematicabyselectingtheMathematicaicon,Mathematica’sstartupwin- dow,“welcomescreen,”isdisplayed,asillustratedinthefollowingscreenshot. From the startup window, you can perform a variety of actions such as creating a new notebook. For example, selecting New Document generates a new Mathematica note- book. 4 MathematicabyExample Mathematica’sonlinehelpfacilitiesarespectacular.Forbeginningusers,oneofthemore convenientfeaturesarethevariousPalettesthatareavailable.ThePalettesprovideavariety of fill-in-the blank templates to perform a wide variety of action. To access a Palette go to theMathematicamenu,selectPalettesandthenselectagivenPalette.Thefollowingscreen shotsshowtheBasicMathAssistantandClassroomAssistantpalettes. IfyougofurtherintothesubmenuandselectOther...,youwillfindtheAlgebraicMa- ThestandardMathematica nipulationpalette,aslightlydifferentBasicMathInputpalettefromthatmentionedabove, palettesaresummarizedin Fig.1.5. andtheBasicTypesettingpalette.
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