       A couple of questions

• To: mathgroup at smc.vnet.net
• Subject: [mg122223] A couple of questions
• Date: Fri, 21 Oct 2011 06:24:37 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <CAAW96o6gjBkriNiW3eUqk+CWo8wwg_BOY=+bG7cWhWPZ3i7CQQ@mail.gmail.com>

``` Hello,

My name is Vlad, and I (erroneously) contacted the consultation
center for Mathematica instead of you--they gave me some quick answers only.

I first was acquainted with Mathematica in my PreCalc class, and have been>>    using it ever since.  I think it is an excellent tool, especially
for its ability to create didactic visualizations.  I had some

As a Calculus tutor, I wanted to provide my peers with a visual
understanding to the "disk" method of calculating volume for
functions rotated around the x or y axes.  All of the online
demonstrations were very well formatted and looked sharp, but I
wanted the students to be able to input their own functions, so I
made my own Mathematica notebook (attachments).  Is it possible to input a>>    Solve function, looking for x in terms of y, instead of asking for
the inverse?  Every time I did so, my graphs ended up replacing the
variable that was being solved for with the variables being plotted
in 3D.

Also, I only have a vague concept of pure functions, and didn't
really understand their purpose or how they work.  How are they
different from regular functions?  When I saw them being used, they
were really no different than, say, a Table function.

Thanks for the help,

Here is my Mathematica code:

lb[x_] = Lighter[Blue, x];
text[x_] = Style[x, Red, 15, Bold];

DynamicModule[
{func = x^2, mindom = -.1, dom = Sqrt[2.], minydom = -2, ydom = 2,
xtrue = True, mesh = None, funcy = Sqrt[y], cyl = 3, vol = True,
a = 2., b = 4.},
Panel[Grid[{{Grid[{{
Grid[{{Text["  f(x)"], InputField[Dynamic[func]]},
{Text["  \!\(\*SuperscriptBox[\(f\), \(-1\)]\)(y)"],
InputField[Dynamic[funcy]]},
{Text[" x-Range"],
Grid[{{
Slider[Dynamic[mindom], {-2 Pi, -1*^-5},
ImageSize -> 100],
Slider[Dynamic[dom], {1*^-5, 2 Pi},
ImageSize -> 100]}}]},
{Text[" y-Range"],
Grid[{{Slider[Dynamic[minydom], {-2 Pi, -1*^-5},
ImageSize -> 100],
Slider[Dynamic[ydom], {1*^-5, 2 Pi},
ImageSize -> 100]}}]},
{Grid[{{Text[" Mesh"],
Checkbox[Dynamic[mesh], {None, 5}]}}],
Grid[{{Text[" Show volumes"], Checkbox[Dynamic[vol]]}}]},
{Text[" Cylinders"], Slider[Dynamic[cyl], {1, 17, 1}]},
{Grid[{{Text[" Lower Limit"],
InputField[Dynamic[a], FieldSize -> 3]}}],

Grid[{{Text[" Upper Limit"],
InputField[Dynamic[b], FieldSize -> 3]}}]}},
Background -> {None, Table[lb[k], {k, 0.6, .9, .05}]},
Spacings -> 3]}, {Dynamic[
Plot[func, {x, mindom, dom}, PlotRange -> {minydom, ydom},
ImageSize -> 200, AxesLabel -> {"x", "y"}]]}}],
Grid[{{SetterBar[
Dynamic[xtrue], {True -> " x Rotation ",
False -> " y Rotation "}]},
{Grid[{{Text[" Inscribe"],
Checkbox[Dynamic[insc], {True, False}]}}]}, {
Dynamic[If[xtrue,
Grid[{{

Plot3D[{Sqrt[func^2 - y^2], -Sqrt[func^2 - y^2]}, {x,
mindom, dom}, {y, minydom, ydom},
Background -> lb[.95], PlotRange -> ydom, Mesh -> mesh,
PlotStyle -> Opacity[.7], Axes -> True,
AxesOrigin -> {0, 0, 0}, Boxed -> False,
AxesLabel -> {text["x"], text["y"], text["z"]},
Ticks -> None],
Dynamic[Graphics3D[Table[{Hue[n], Opacity[.9],

Cylinder[{{n, 0, 0}, {n + (dom - mindom)/cyl, 0,
0}}, Abs[ func /. x -> (n + (dom - mindom)/cyl)]]},
{n, a, b (cyl - 1)/cyl, (dom - mindom)/cyl}] //
Flatten, Ticks -> None, Background -> lb[.95],
AxesLabel -> {text["x"], text["y"], text["z"]},
Boxed -> False, Axes -> True, AxesOrigin -> {0, 0, 0},
PlotRange -> {{mindom, dom}, {minydom, ydom}, {-ydom,
ydom}}]
]}, Flatten[{If[vol, {Grid[{{Style[\!\(
\*UnderoverscriptBox[\("\<\[Integral]\>"\), \(a\), \(b\)], \
Medium\)],
Style[\[Pi] (func)^2 \[DifferentialD]x,
Medium]}, {Abs[
NIntegrate[Pi func^2, {x, a, b}] // Quiet]}}],
Grid[{{Style[
\!\(\*UnderscriptBox[
OverscriptBox[\("\<\[Sum]\>"\), \(cyl\)], \("\<j=1\>"\)]\), Medium],
Style[\[Pi] Subscript[r, j]^2 Subscript[h, j],
Medium]}, {Total[
Table[Abs[
Pi (b - a)/
cyl (1.) (func /. x -> (n + (b - a)/cyl))^2], {n,
a, b (cyl - 1)/cyl, (b - a)/cyl}]]}}]}]}]}]
, Grid[{{

Plot3D[{Sqrt[(funcy)^2 -
x^2], -Sqrt[(funcy)^2 - x^2]}, {x, mindom, dom}, {y,
minydom, ydom}, Background -> lb[.95],
PlotRange -> dom, Mesh -> mesh,
PlotStyle -> Opacity[.7], Axes -> True,
AxesOrigin -> {0, 0, 0}, Boxed -> False,
AxesLabel -> {text["x"], text["y"], text["z"]},
Ticks -> None],
Dynamic[Graphics3D[Table[{Hue[n], Opacity[.9],

Cylinder[{{0, n, 0}, {0, n + (b - a)/cyl, 0}},
Abs[funcy /. y -> (n + (b - a)/cyl)]]},
{n, a, b (cyl - 1)/cyl, (b - a)/cyl}] // Flatten,
Ticks -> None,
AxesLabel -> {text["x"], text["y"], text["z"]},
Background -> lb[.95], Boxed -> False, Axes -> True,
AxesOrigin -> {0, 0, 0},
PlotRange -> {{mindom, dom}, {minydom, ydom}, {-dom,
dom}}]]
}, {If[vol, {Grid[{{Style[\!\(
\*UnderoverscriptBox[\("\<\[Integral]\>"\), \(a\), \(b\)], \
Medium\)],
Style[\[Pi] (funcy)^2 \[DifferentialD]y,
Medium]}, {Abs[
NIntegrate[Pi funcy^2, {y, a, b}] // Quiet]}}],
Grid[{{Style[
\!\(\*UnderscriptBox[
OverscriptBox[\("\<\[Sum]\>"\), \(cyl\)], \("\<j=1\>"\)]\), Medium],
Style[\[Pi] Subscript[r, j]^2 Subscript[h, j],
Medium]}, {Total[
Table[Abs[
Pi (1.) (b - a)/
cyl (funcy /. y -> (n + (b - a)/cyl))^2], {n, a,
b (cyl - 1)/cyl, (b - a)/cyl}]]}}]}]} // Flatten}]

]]
}}]
}}], Background -> lb[.95]]]

> On 10/20/11 10:48, Feinberg, Vladimir wrote:
>
>> Sorry, forgot the file!
>>
>> On Thu, Oct 20, 2011 at 7:47 AM, Feinberg, Vladimir
>> wrote:
>>
>>    Hello,
>>
>>    My name is Vlad, and I (erroneously) contacted the consultation
>>    center for Mathematica instead of you--they gave me some quick answers only.
>>
>>    I first was acquainted with Mathematica in my PreCalc class, and have been
>>    using it ever since.  I think it is an excellent tool, especially
>>    for its ability to create didactic visualizations.  I had some
>>
>>    As a Calculus tutor, I wanted to provide my peers with a visual
>>    understanding to the "disk" method of calculating volume for
>>    functions rotated around the x or y axes.  All of the online
>>    demonstrations were very well formatted and looked sharp, but I
>>    wanted the students to be able to input their own functions, so I
>>    made my own Mathematica notebook (attachments).  Is it possible to input a
>>    Solve function, looking for x in terms of y, instead of asking for
>>    the inverse?  Every time I did so, my graphs ended up replacing the
>>    variable that was being solved for with the variables being plotted
>>    in 3D.
>>
>>    Also, I only have a vague concept of pure functions, and didn't
>>    really understand their purpose or how they work.  How are they
>>    different from regular functions?  When I saw them being used, they
>>    were really no different than, say, a Table function.
>>
>>    Thanks for the help,