I should have attributed the quotations. From: Dusko Pavlovic <dusko@kestrel.edu> Date: Wed, 05 Oct 2011 13:52:25 +0100
... the function x sin(x), i think, ...
Correct.
... as studied by undergraduates in calculus I.
According to the course descriptions here at UBC, there is at least a mention of series in first year courses. Fourier and other series appear in 2nd & 3rd years.
... might be worth while to rework widder's book on transform theory coalgebraically.
Engineer speaking. Mathematicians, don't be too critical. What I recall from a brief study decades ago is that each of the familiar series--Taylor, Laurent, Fourier & etc.--is based upon a set of orthogonal functions. So I wondered whether the category of sets of orthogonal functions has been thoroughly studied. Such a study might show the necessity of infinite series to represent the inverses of some functions. Wishful thinking? Thanks, ... Peter E. -- Telephone 1 360 450 2132. bcc: peasthope at shaw.ca Shop pages http://carnot.yi.org/ accessible as long as the old drives survive. Personal pages http://members.shaw.ca/peasthope/ . [For admin and other information see: http://www.mta.ca/~cat-dist/ ]