Operator Calculus:   Linear Operator Rules

Does Mathematica  apply the Fourier Transform/Derivative Rule Automagically?



It does as of version 5.0! .



Does  Mathematica apply the rules according to the Fourier Transform being a linear operator?



Apparently not--so we make some rules that can be applied. It may be instructive to see how to do this.

Two rules are defined so as to factor out non-dependent variables and apply the distribution rules for linear operators




Try them out:





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