A couple of questions

*To*: mathgroup at smc.vnet.net*Subject*: [mg122223] A couple of questions*From*: "Feinberg, Vladimir" <13vladimirf at students.harker.org>*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 questions about Mathematica: 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, Vlad 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 >> <13vladimirf at students.harker.**org <13vladimirf at students.harker.org> >> <mailto:13vladimirf at students.**harker.org<13vladimirf at students.harker.org>>> >> 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 >> questions about Mathematica: >> >> 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, >> Vlad >> Vlad >>