AWorkbookforDifferentialEquations
- 作者
- 出版社 Wiley
- 出版时间 2009年12月
- ISBN 9780470447512
- 定价 647.80
内容简介
Anaccessibleandhands-onapproachtomodelingandpredictingreal-worldphenomenausingdifferentialequationsAWorkbookforDifferentialEquationspresentsaninteractiveintroductiontofundamentalsolutionmethodsforordinarydifferentialequations.Theauthoremphasizestheimportanceofmanuallyworkingthroughcomputationsandmodels,ratherthansimplyreadingormemorizingformulas.Utilizingreal-worldapplicationsfromspring-masssystemsandcircuitstovibratingstringsandanoverviewofthehydrogenatom,thebookconnectsmodernresearchwiththepresentedtopics,includingfirstorderequations,constantcoefficientequations,Laplacetransforms,partialdifferentialequations,seriessolutions,systems,andnumericalmethods.Theresultisauniqueguidetounderstandingthesignificanceofdifferentialequationsinmathematics,science,andengineering.Theworkbookcontainsmodulesthatinvolvereadersinasmanywaysaspossible,andeachmodulebeginswith"Prerequisites"and"LearningObjectives"sectionsthatoutlineboththeskillsneededtounderstandthepresentedmaterialandwhatnewskillswillbeobtainedbytheconclusionofthemodule.Detailedapplicationsareintertwinedinthediscussion,motivatingtheinvestigationofnewclassesofdifferentialequationsandtheiraccompanyingtechniques.Introductorymodelingsectionsdiscussapplicationsandwhycertainknownsolutiontechniquesmaynotbeenoughtosuccessfullyanalyzecertainsituations.Almosteverymoduleconcludeswithasectionthatcontainsvariousprojects,rangingfromprogrammingtaskstotheoreticalinvestigations.Thebookisspecificallydesignedtopromotethedevelopmentofeffectivemathematicalreadinghabitssuchasdouble-checkingresultsandfillinginomittedstepsinacomputation.Ratherthanprovidelengthyexplanationsofwhatreadersshoulddo,goodhabitsaredemonstratedinshortsections,andawiderangeofexercisesprovidetheopportunitytotestreadercomprehensionoftheconceptsandtechniques.Richillustrations,highlightednotes,andboxedcommentsofferilluminatingexplanationsofthecomputations.Thematerialisnotspecifictoanyoneparticularsoftwarepackage,andasaresult,necessaryalgorithmscanbeimplementedinvariousprograms,includingMathematica®,Maple,andMathcad®.Thebook'srelatedWebsitefeaturessupplementalslidesaswellasvideosthatdiscussadditionaltopicssuchashomogeneousfirstorderequations,thegeneralsolutionofseparabledifferentialequations,andthederivationofthedifferentialequationsforamulti-loopcircuit.Inaddition,twentyactivitiesareincludedatthebackofthebook,allowingforfurtherpracticeofdiscussedtopicswhetherintheclassroomorforself-study.Withitsnumerouspedagogicalfeaturesthatconsistentlyengagereaders,AWorkbookforDifferentialEquationsisanexcellentbookforintroductorycoursesindifferentialequationsandappliedmathematicsattheundergraduatelevel.Itisalsoasuitablereferenceforprofessionalsinallareasofscience,physics,andengineering.
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