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TheoryAnalysis,,,MathematicsAnalysisModelIntroductionEquationDescription,MathematicsAnalysis,1.Introducethemeandobjective.2.Describerelativehypothesis,conditionordefinition.3.Presentprimaryproblemsorbasicequations.4.Analyzeandgetsomeresults.5.Discussorinferaccordingtoaboveresults.3-5mayrepeat.,1.Describebackgroundortheorybasisofthemodel.[usereferences]2.Listandanalyzesomebasicequations.3.Describethemodelindetail.4.Explainordiscusstheimportantcharacteristicsofthemodel.5.Depicthowtoapplythemodelincertainsituationwithanexample.2-5repeatforeachpart,subtheme,orstageofthemodel.,ModelIntroduction,LayoutPunctuation,EquationDescription,Notice,Describethedefinitionofhypothesisorconceptsbeforeusingthem.Presenttheproblembeforedepictingtheequationsused.Stateeachsubthemeofthetheorywithsummaryattheendofeachstatement.Expresstherelationshipamongsubthemesifnecessary.,Tense:Presenttenseforfacts.(most)E.g.ThesolutioncanbeobtainedbysolvingEq.(2).Futuretensefornewthemedescriptioninnewparagraph.E.g.Wewillsolvethisprobleminthecontextofthefollowingmodel.IfX=0,thentheprocesswill…,,PasttenseforPastworkorexperimentresultsoftheauthorofthispaper.Hypothesisoforiginalauthors.,Voice:Passivevoice.Avoidusing:Itis…Thereis/are…“We”assubject.,Sentences:Itissupposedthat….Wesupposethat…(good)Letussupposethat…Supposethat…(good),AftersubstitutingthistermforyinEquation(4),theequationcanberewrittenasfollows.AftersubstitutingthistermforyinEquation(4),Wecanrewritetheequationasfollows.(good)IfthistermissubstitutedforyinEquation(4),theequationcanberewrittenasfollows.(good)SubstitutingthistermforyinEquation(4)yieldsthefollowingequation.(good),Therelationshipbetweenxandyisnowconsidered.Nowletusconsidertherelationshipbetweenxandy.(good)Considertherelationshipbetweenxandy.(good)xandyarerelatedinthefollowingway.(good),Samplesentences:Considerthecaseinwhich…Letusnowconsiderthecase…Supposethat…LetdandVbescalingsforthelengthandwidth.Weassumethat…underconsiderationhere.Ifx=1,thenwehavethefollowingequations:(equation)Giventhatm=1.2,weobtain…(equation)TheequationforAg/Atbecomes…(equation)TheequationforAg/Atcanbewritten/expressedas…SubstitutingmintoEquation3,weobtain…Therelationshipbetweenmandnisasfollows.(equation)AisinverselyproportionaltoB,asshownbelow.,Eq.5takestheform..Fromthisequation,therelationbetweenxandycanbeexpressedas…Ifthesamematerialisused,theaboveequationreduceto…WewillnowreduceEq.3toasimplerform.OnsubstitutingthisequationintoEq.16andsolvingforx2,…The…isdefinedas..The…isgivenby…UponperformingtheintegrationusingEq.19,substitutinga+bforx,letz=c/d,andsimplifying,…WewillnowintegrateEquation2inordertoderivethesolution.WecannowderivethesolutiontoEquation2.IfEq.16issolvedforX,…,