Laplace Transform - Efficiently via Maple

Consider what a STEM student must interiorize when first exposed to the Laplace transform: Its definition, and examples worked out from first principles. (This is more calculus than anything.) The operational laws: multiplication in t (the time domain) corresponds to differentiation in s (the transform variable); differentiation in t corresponds to multiplication in s. More operational laws: division in t corresponds to integration in s; integration in t corresponds to division in s. Then there are two or three shifting laws. And the rule for taking the transform of a periodic function. Don't forget the convolution product and the convolution theorem. And what about the Dirac delta "function"? All this in at maybe 3 or 4 weeks. And if taught with pencil-and-paper technology, then in addition to facility with the calculus, the student must also be algebraically nimble. And speed this up if the Laplace transform is to be used in a differential equations class.
Let's take a look at the wealth of material a student must absorb in a first exposure to the Laplace transform taught with the technology of pencil-and-paper, and then look at how much more efficiently the teaching, learning, and doing of the material can be accomplished with the technology of Maple.
And finally, let us ask ourselves why, in the 21st Century, we still do this with pencil-and-paper. Is it because the test is the tail wagging the dog?
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