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1、transform—libraryforintegraltransformsTableofcontentsPreface.....................................iiHelpPagestransform::fourier,transform::invfourier—FourierandinverseFouriertransform..............................1transform::laplace,transform::invlaplace—LaplaceandinverseLaplacetransform...
2、...........................3IntroductionThetransformlibraryprovidessomeintegraltransformations.Thepackagefunctionsarecalledusingthepackagenametransformandthenameofthefunction.E.g.,use>>transform::fourier(exp(-t^2),t,s)tocomputetheFouriertransformofe−t2withrespecttotatthepoints.Thismechanis
3、mavoidsnamingconflictswithotherlibraryfunctions.Ifthisisfoundtobeinconvenient,thentheroutinesofthetransformpackagemaybeexportedviaexport.E.g.,aftercalling>>export(transform,fourier)thefunctiontransform::fouriermaybecalleddirectly:>>fourier(exp(-t^2),t,s)Allroutinesofthetransformpackageareex
4、portedsimultaneouslyby>>export(transform)Thefunctionsavailableinthetransformlibrarycanbelistedwith:>>info(transform)iitransform::fourier,transform::invfourier–FourierandinverseFouriertransformR∞transform::fourier(f,t,s)computestheFouriertransformfeistdt−∞oftheexpressionf=f(t)withrespecttot
5、hevariabletatthepoints.1R∞−iSTtransform::invfourier(F,S,T)computestheinverseFouriertransformFedS2π−∞oftheexpressionF=F(S)withrespecttothevariableSatthepointT.Call(s):AAtransform::fourier(f,t,s)transform::invfourier(F,S,T)Parameters:f,F—arithmeticalexpressionst,S—identifiers(thetransformatio
6、nvariables)s,T—arithmeticalexpressions(theevaluationpoints)ReturnValue:anarithmeticalexpressionOverloadableby:f,FRelatedFunctions:numeric::fft,numeric::invfftDetails:AAnunevaluatedfunctioncallisreturned,ifnoexplicitrepresentationofAthetransformisfound.transform::invfourier(F,S,T)iscomputed
7、astransform::fourier(F,S,−T)/2/PI.Thisresultisreturned,ifnoexplicitrepresentationofthetransformationAisfound.ThediscreteFouriertransformisimplementedbythefunctionsnumeric::fftandnumeric::invfft.Example1.ThefollowingcallproducestheFouriertransformasanexpres-sio
