       Re: how to differentiate a list?

• To: mathgroup at smc.vnet.net
• Subject: [mg25956] Re: how to differentiate a list?
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Tue, 14 Nov 2000 03:46:50 -0500 (EST)
• References: <8ug96o\$id9@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Rob:
If you will have your list, say
data = Table[s[i], {i, 0, 1, .2}]

{s, s[0.2], s[0.4], s[0.6], s[0.8], s[1.]}

Then

Drop[data, 1] - Drop[data, -1]

{-s + s[0.2], -s[0.2] + s[0.4], -s[0.4] + s[0.6], -s[0.6] +
s[0.8], -s[0.8] + s[1.]}

or

ListConvolve[ {1, -1}, data]

{-s + s[0.2], -s[0.2] + s[0.4], -s[0.4] + s[0.6], -s[0.6] +
s[0.8], -s[0.8] + s[1.]}

Alternatively, with numerical data, we can get an interpolating function and
differentiate it.

data2 = Table[{i, Sin[i]}, {i, 0, 2 Pi, 0.1  Pi}];

f = Interpolation[data2]

InterpolatingFunction[{{0., 6.28319}}, "<>"]

Plot[{f[x], f'[x]}, {x, 0, 2Pi}]

--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

"Rob" <piovere at pdq.net> wrote in message news:8ug96o\$id9 at smc.vnet.net...
> I needed to get the derivative of a time varying pulse to do some
> numerical
> operations.  As seen below, the only way I could figure how to do it
> was to generate two lists, shifted by one sample and then subtract them:
>
> ***************
> del = 0.002; a = 12\[Pi]; b = \[Pi];
> ( s[t] is a function of t defining the pulse )
>
> sd = Table[N[s[t]], {t, 0, 1, del}];
> sd1 = Table[N[s[t]], {t, del, 1 + del, del}];
> diff = sd - sd1;
> ****************
>
> I looked all over and I didn't find a list operation available to do
> this. I bet
> you Mathematica gurus know how to do this.  If so, could you enlighten me?
>
> Thanks, Rob
>
>
>

```

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