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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)
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• Delivered-to: l-mathgroup@wolfram.com
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• 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.
>

• References:
  • inserting an equation and plotting it
    • From: Abdo Adam <abdo.d12@hotmail.com>