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Re: inserting an equation and plotting it
*To*: mathgroup at smc.vnet.net
*Subject*: [mg128801] Re: inserting an equation and plotting it
*From*: Bob Hanlon <hanlonr357 at gmail.com>
*Date*: Tue, 27 Nov 2012 03:32:09 -0500 (EST)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*Delivered-to*: l-mathgroup@wolfram.com
*Delivered-to*: mathgroup-newout@smc.vnet.net
*Delivered-to*: mathgroup-newsend@smc.vnet.net
*References*: <20121126042737.6C81468DB@smc.vnet.net>
Square brackets are only used for enclosing function arguments and
curly brackets are only used for lists. Periods do not belong in
symbolic expressions unless you are doing dot products.
a[q_, m_] = Module[
{r = q/m, s},
s = Sqrt[1 - r^2];
2 Pi/(m (Pi + r/2 - ArcCos[s] + (1 - s)/r))]
(2*Pi)/(m*(Pi + q/(2*m) +
(m*(1 - Sqrt[1 - q^2/m^2]))/
q - ArcCos[Sqrt[
1 - q^2/m^2]]))
The case for q=0 must be handed in the limit
Limit[a[q, m], q -> 0]
2/m
a[q_ /; q == 0, m_] = 2/m;
Plot[Evaluate[
Table[a[q, m], {q, 0, 1, 0.1}]],
{m, 1, 5},
AxesLabel -> {"m", "a[q,m]"}]
The curves essentially overlap, zooming in to see the separate curves:
Plot[
Evaluate[
Table[
Tooltip[a[q, m], "q = " <> ToString[q]], {q, 0, 1, 0.1}]],
{m, 1, 1.01},
AxesLabel -> {"m", "a[q,m]"}]
Alternatively, use Manipulate to look at the separate curves individually.
Manipulate[
Plot[a[q, m], {m, 1, 5},
AxesLabel -> {"m", "a[q,m]"},
PlotRange -> {0, 2.1}],
{q, 0, 1, 0.1, Appearance -> "Labeled"}]
Similarly for q as the independent variable
Plot[
Evaluate[
Table[
Tooltip[a[q, m], "m = " <> ToString[m]],
{m, 1, 5, 0.5}]],
{q, 0, 1},
AxesLabel -> {"q", "a[q,m]"},
PlotRange -> {0, 2.1}]
Manipulate[
Plot[a[q, m], {q, 0, 1},
AxesLabel -> {"q", "a[q,m]"},
PlotRange -> {0, 2.1}],
{m, 1, 5, 0.05, Appearance -> "Labeled"}]
Combining all into a single graphic
Manipulate[
Show[
Plot3D[a[qv, mv],
{mv, 1, 5}, {qv, 0, 1}],
Graphics3D[
{Red,
AbsoluteThickness[2],
Line[{m, #[[1]], #[[2]]} & /@
Cases[
Plot[a[qv, m], {qv, 0, 1}],
Line[pts_] :> pts, Infinity][[1]]],
Line[{#[[1]], q, #[[2]]} & /@
Cases[
Plot[a[q, mv], {mv, 1, 5}],
Line[pts_] :> pts, Infinity][[1]]],
Blue,
AbsolutePointSize[10],
Tooltip[
Point[{m, q, a[q, m] + 0.01}],
Style[
"a[q, m] = " <> ToString[a[q, m]],
14]]}],
AxesLabel -> (Style[#, Bold, 12] & /@
{"m", " q", "a[q, m] "})],
{{q, 0.5}, 0, 1, 0.02, Appearance -> "Labeled"},
{{m, 3}, 1, 5, 0.05, Appearance -> "Labeled"}]
Bob Hanlon
On Sun, Nov 25, 2012 at 11:27 PM, Abdo Adam <abdo.d12 at hotmail.com> wrote:
> i'm trying to insert an equation and plot it, but i couldn't because i keep getting errors like : matrix dimensions must agree, or inner matrix dimensions must agree.
>
> http://www4.0zz0.com/2012/11/25/10/272913238.png
> this is the equation. M has a value of 1 to 5 with an increment of 0.5. Q has a value of 0 to 1 with an increment of 0.1.
>
> http://www4.0zz0.com/2012/11/25/10/700692428.png
> the plot is something like this.
>
> i tried to split the equation into parts, so it would be easier for me to insert it
> i'm having a problem with the last part, i get this error
>
> e=q./m(1-sqrt(1-(q./m).^2));
>
> Subscript indices must either be real positive integers or logicals.
>
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