Re: Very very basic question about Mathematica expressions
- To: mathgroup at smc.vnet.net
- Subject: [mg111126] Re: Very very basic question about Mathematica expressions
- From: Helen Read <hpr at together.net>
- Date: Wed, 21 Jul 2010 07:12:52 -0400 (EDT)
- References: <i23k1j$epv$1@smc.vnet.net>
- Reply-to: HPR <read at math.uvm.edu>
On 7/20/2010 3:42 AM, Sam Takoy wrote:
> Hi,
>
> I find that I don't understand a very basic thing about the building
> blocks of Mathematica.
>
> When the first command is
>
> s = x + h
>
> I figured that (string?) "s" represents (string?) "x+h".
To make it a string, i.e., a sequence of text characters, you would
enter the following.
s="x+h"
Strings are useful for lots of things, but I don't think a string is
what you intend. What you have instead is an expression.
> But then by doesn't this work:
>
> Manipulate[ Plot[s, {x, 0, h}], {h, 0.1, 1}]
>
> Many thanks in advance!
Manipulate needs to know that s is a function of both x and h.
Clear[s]
s[x_,h_]:=x+h
Also you should put an explicit PlotRange in your Plot, so that
Manipulate doesn't go changing the scale on you.
Try it without a PlotRange:
Manipulate[
Plot[s[x, h], {x, 0, h}]
And see how much better it is with one.
Manipulate[
Plot[s[x, h], {x, 0, h}, PlotRange -> {{0, 1}, {0, 1}}], {h, 0.1, 1}]
Defining functions is a very basic idea in Mathematica, and worth
getting used to.
For example, suppose you want to find the extrema of the function
f(x)= -84 x + 9 x^2 + 4 x^3 + 25
So define it as a function.
f[x_] := -84 x + 9 x^2 + 4 x^3 + 25
Plot[f[x], {x, -10, 10}]
Might want to see the 1st derivative along with it.
Plot[{f[x], f'[x]}, {x, -10, 10}]
Solve[f'[x] == 0, x]
f[-7/2]
f[2]
--
Helen Read
University of Vermont