数学专业英语论文.doc

数学专业英语论文.doc课文9・BTerminologyandnotationwhenweworkwithadifferentialequationsuchas(),itiscustomarytowriteyinplaceof/(x)andy'inplaceoff(x),thehigherderivativesbeingdenotedbyy”,y”‘,,otherletterssuchasu,v,z,,()isfirst-orderequationwhichmaybewrittenasy-'=x,y+sin(xy”)-orderequationswhichcanbesolvedfbryfandwrittenasfollows:ygy),Wheretheexpression./(x,y)=Y(x)willbecalledasolutionof()onanintervalIifthefunctionYandanditsderivativeYsatisfytherelationV=/[x』(x)]/(x,y),es),=0x),Say,(),everysolutionof()isincludedintheformula尸jQ(x)dx+C,whereCisanyconstant(usuallycalledanarbitraryconstantofintegration).Thedifferentialequation()hasinfinitelymany课文9-B术语和符号当我们在求解像()式的微分方程时,习惯用顶代替Rx),用),,(x),用高阶导数和"〃等表示。当然,其他的字母如*等等,同样可以用来代替方微分方程和阶数指的是现在其中的高阶导数的阶。例如,()式是一个一次方程可以写成微分方程 y'=x3y+sin(xy“)是一个二阶的。在这章我们将会学习到可以求解S的…阶微分方程。一阶方程可以被写成这样:)F,y),其中,右边有各个特殊形式表示。如果对于区间I