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    <p>You have a list of {date,value} pairs so if you <a href="http://reference.wolfram.com/mathematica/ref/Transpose.html" rel="nofollow noreferrer">Transpose</a> that you'll have a list of two lists -- the first a list of dates and the second a list of corresponding values. You can then take the <a href="http://reference.wolfram.com/mathematica/ref/Differences.html" rel="nofollow noreferrer">Differences</a> of the values, <a href="http://reference.wolfram.com/mathematica/ref/Prepend.html" rel="nofollow noreferrer">Prepend</a> 0, and then Transpose again to get back to a list of pairs.</p> <p>In code,</p> <pre><code>data = {{{1971,1,31,0,0,0}, 1.0118}, {{1971,2,28,0,0,0}, 1.0075}, {{2010,5,31,0,0,0}, 1.0403}} {dates, values} = Transpose[data]; diffs = Prepend[Differences[values], 0]; answer = Transpose[{dates, diffs}] </code></pre> <p>which returns:</p> <pre><code>{{{1971,1,31,0,0,0}, 0}, {{1971,2,28,0,0,0}, -0.0043}, {{2010,5,31,0,0,0}, 0.0328}} </code></pre> <p>To wrap that up into a single function, with thanks to <a href="https://stackoverflow.com/users/212538/janus">Janus</a> for the idea:</p> <pre><code>taildiffs[data_]:= Transpose @ {#1, Prepend[Differences[#2], 0]}&amp; @@ Transpose@data </code></pre> <p>Note that the <code>... #1 ... #2 ... &amp;</code> construct is a pure function:</p> <p><a href="http://reference.wolfram.com/mathematica/ref/Function.html" rel="nofollow noreferrer">http://reference.wolfram.com/mathematica/ref/Function.html</a></p> <p>The <code>f@x</code> syntax is simply shorthand for <code>f[x]</code>.</p> <p>Finally, <code>f@@list</code> is shorthand for <code>Apply[f, list]</code>:</p> <p><a href="http://reference.wolfram.com/mathematica/ref/Apply.html" rel="nofollow noreferrer">http://reference.wolfram.com/mathematica/ref/Apply.html</a></p> <p>So taildiffs as defined above is just a terse (perhaps cryptic) version of this:</p> <pre><code>Apply[Transpose[Function[{x,y}, {x, Prepend[Differences[y],0]}], Transpose[data]] </code></pre>
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    1. POHow to subtract specific elements in a list using functional programming in Mathematica?
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    1. POHow to subtract specific elements in a list using functional programming in Mathematica?
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    1. CO+1 This is much clearer (and probably faster) than mine.
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    2. COSo, to make sure that I am making progress in understanding the Functional Notation, the singe function works like this: 1) data is Transposed into two lists, #1 and #2. 2) Those two lists are applied in the following manner; #1 is left alone, and #2 is Differenced and Prepended with 0. 3) #1 and the modified #2 are then Transposed back into a single list. Is that correct?
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    3. COExactly. Well said. You should know more generally that, for example, foo[#2,#1]& is a pure function of two arguments that calls foo on those two arguments (in reverse order). Other fancy syntax there is the @ and @@. Let me append something to the answer to explain those...
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