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1、数学常用短语与从句Phrasesorclausesfrequentlyusedinmathematics常见的涉及运算的短语或句子1.Differentiatebothsidesoftheequationandweget...Integratebothsidesoftheequationandweget…2.Differentiatingbothsidesoftheequation,weget...Integratingbothsidesoftheequation,weget...3.Add(A)to(B)andwehave…(其中(A)、(B)为某些表达式，如不等式、等式、方程等
2、，下同)4.Subtract(B)from(A)andwehave…5.Multiplyingeachtermoftheequationby…，weobtain...6.Dividingtheequationthroughby…，wehave…7.(A)and(B)togethergive...(A)and(B)togetheryield...(A)and(B)togetherimply...&Comparing(A)with(B),itiseasytoseethat...9・Substituting(A)into(B),weobtain...10.Eliminating(thep
3、arameter)tfrom(A)and(B),wehave...11.Byintroducinganewvariablewecanthenrewrite(A)asfollowsByintroducinganewvariable•••,wecanthenrewrite(A)inthefollowingform12.Byasimplecalculation,weobtainfrom(A)...定理证明过程中常见的短语和句子1•下面的句型可用来表达“根据什么即可得到什么”的意思Accordingtodefinition,itfollows...Accordingtohypothesis
4、,itfollows・・・Accordingtoasssumptions,itfollows•…Accordingtotheorem(N),itfollows•・・Accordingtolemma(A),itfollows...Accordingtocorollary(B),itfollows••・Accordingtotheremark,itfollows・・・Accordingtothefactthat…，itfollows…(可以把上面的"accordingto”换成“by”)Sinceitfollows...2.如果一个论断可以通过一些简单运算或简单推理而获得，rti于这些
5、运算或推理比较简单,读者可以白行推算，因而只需直接写出论断来，这时可用下面句型：(1)Itiseasytoseethat...Itiseasytoshowthat...Itiseasytoprovethat...Itiseasytoverifythat...Itiseasytocheckthat…(2)Itcaneasilybeseenthat...Itcaneasilybeshownthat..・Itcaneasilybeverifiedthat...Itcaneasilybecheckedthat...2.如果所要提及的结论比较显浅，或是众所周知，无需作进一步的证明，这时可用下
6、面句型:(1)Itisclearthat...Itisobviousthat...Itisevidentthat•..Itiswell-knownthat...(2)Clearly,...Obviously,...Evidently,…3.为了证明一个定理有时需要引进辅助函数，这时可用下面句型：Letusfirstdefinethefunction...Letusoduceanewfunction...Letusconsiderthefunction…Letusfirstinvestigatethefunction...Let...Set...Define...Put…Consid
7、er...2.在一个定理中，有几个结论需要证明，英中有些结论比较明显，可不用证明，仅需证明余下结论即可，这时可用下面句型：Since(A)and(B)areobvious,weneedonlyprove(C).Since(A)and(B)aretrivial,weneedonlyprove(C).Since(A)and(B)aretrivial,itsufficestoprove(C)3.为了证明一个定理，有时我们并不是直接去证明，而是证明一个新的论断，一旦新的论断得
