Re: Functions of Functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg49653] Re: Functions of Functions*From*: drbob at bigfoot.com (Bobby R. Treat)*Date*: Mon, 26 Jul 2004 04:01:57 -0400 (EDT)*References*: <200407240747.DAA05846@smc.vnet.net> <cdvmje$7lr$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Sorry, that didn't make any sense, because I missed a line of Michael's code. David Park gave a much better answer. Bobby DrBob <drbob at bigfoot.com> wrote in message news:<cdvmje$7lr$1 at smc.vnet.net>... > Here's your code again: > > Clear[a, b, c, x] > a[x_] := Sin[x] + x^3/2 > c = b[a] > c[x] > > It's clear that you've defined a to be a function. A named pattern (x_) is used on both sides of the SetDelayed. > > But you didn't do anything like that in defining c; no named patterns at all. > > So how can anyone know what you want c[x] to be? If I could guess, I'd show you how to accomplish it. > > Slightly more subtle is the point that, as you've defined it, a isn't a function of x; a[x] is. a[y] is a function of y, a[z] depends on z, et cetera. > > But a isn't a function at all, except when it's given an argument. That's why, once again, there's no mention of x in your definition of c. > > Bobby > > On Sat, 24 Jul 2004 03:47:29 -0400 (EDT), Michael J Person <mjperson at mit.edu> wrote: > > > Hello, > > > > I was wondering if anyone could help me with this. > > > > I've gone through the book and help files as best I can, but > > can't seem to figure out why the following doesn't work: > > > > I'm trying to work with functions that take functions > > as parameters and return other functions. > > > > Below is an example... > > > > (*clear stuff*) > > Clear[a, b, c, x] > > > > > > (*Define a functions a*) > > \!\(a[x_] := \((Sin[x] + x\^3\/2)\)\) > > > > > > (*define a function of functions*) > > \!\(b[f_] = \((f'' + \(3\ f'\)\/2 + 5 f)\)\) > > > > (*apply the functional function to a*) > > c = b[a] > > > > (*Try to apply the resulting function to something*) > > c[x] > > > > This last step never gives me the results I'd expect by applying > > the derivatives of a to x... > > > > Can anyone tell me where I've gone horribly wrong? > > > > Thanks much, > > > > MJ Person > > mjperson at mit.edu > > > > > >

**References**:**Functions of Functions***From:*mjperson@mit.edu (Michael J Person)

**Re: Bug? Wrong result from infinite sum.**

**Slow LinearSolve.**

**Re: Functions of Functions**

**about principal components analysis (PCA)**