(*^ ::[ frontEndVersion = "Macintosh Mathematica Notebook Front End Version 2.1"; macintoshStandardFontEncoding; paletteColors = 128; currentKernel; fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M18, O486, bold, L3, r58981, g58981, b58981, e8, 24, "New York"; ; fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M18, O486, bold, L2, r58981, g58981, b58981, e6, 18, "New York"; ; fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M18, O486, bold, L2, r58981, g58981, b58981, e6, 14, "New York"; ; fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M18, O486, bold, L2, a10, 14, "New York"; ; fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M18, O486, bold, L2, a10, 12, "CalcAndMath"; ; fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, O486, bold, L2, a10, 12, "CalcAndMath"; ; fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M18, O486, L2, 12, "CalcAndMath"; ; fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M18, O486, B65535, L2, 12, "CalcAndMath"; ; fontset = input, noPageBreakInGroup, preserveAspect, groupLikeInput, M36, N23, O486, bold, L2, 12, "Courier"; ; fontset = output, output, inactive, noPageBreakInGroup, preserveAspect, groupLikeOutput, M36, N23, O486, L2, 12, "Courier"; ; fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M18, N23, O486, R65535, L2, 12, "Courier"; ; fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M18, N23, O486, L2, 12, "Courier"; ; fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M18, N23, O486, L2, 12, "Courier"; ; fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M18, O486, l34, w282, h287, L2, 12, "Courier"; ; fontset = name, inactive, nowordwrap, nohscroll, noKeepOnOnePage, preserveAspect, M18, O486, italic, B65535, L2, 10, "Geneva"; ; fontset = header, inactive, noKeepOnOnePage, preserveAspect, M18, O486, L2, 10, "Times"; ; fontset = leftheader, inactive, M18, O486, L2, 10, "Times"; ; fontset = footer, inactive, noKeepOnOnePage, preserveAspect, center, M18, O486, L2, 12, "Times"; ; fontset = leftfooter, inactive, center, M18, O486, L2, 12, "Times"; ; fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M18, O486, L2, 10, "Geneva"; ; fontset = clipboard, inactive, noKeepOnOnePage, preserveAspect, M18, O486, L2, 12, "New York"; ; fontset = completions, inactive, nowordwrap, noKeepOnOnePage, preserveAspect, M18, O486, L2, 12, "New York"; ; fontset = special1, inactive, nowordwrap, noKeepOnOnePage, preserveAspect, M18, O486, L2, 12, "New York"; ; fontset = special2, inactive, nowordwrap, noKeepOnOnePage, preserveAspect, center, M18, O486, L2, 12, "New York"; ; fontset = special3, inactive, nowordwrap, noKeepOnOnePage, preserveAspect, right, M18, O486, L2, 12, "New York"; ; fontset = special4, inactive, noKeepOnOnePage, preserveAspect, M18, O486, bold, superscript, R21845, G21845, B21845, L2, 12, "C&M"; ; fontset = special5, inactive, noKeepOnOnePage, preserveAspect, M18, O486, bold, superscript, R19708, G31200, B40959, L2, 12, "C&M"; ; ] :[font = title; inactive; dontPreserveAspect; ] Summer Project for Calculus and Mathematica Workshop Jenna Caldwell ;[s] 11:0,2;11,0;19,1;20,0;31,4;34,0;35,5;48,6;59,5;68,0;69,3;84,-1; 7:4,33,24,New York,1,24,0,0,0;1,75,54,Courier,1,72,65535,0,0;1,18,12,Chicago,1,12,0,0,0;1,18,12,New York,1,12,0,0,65535;1,18,12,New York,1,12,0,0,0;2,32,23,New York,1,23,0,0,0;1,32,23,New York,3,23,0,0,0; :[font = postscript; PICT; formatAsPICT; output; inactive; Cclosed; preserveAspect; pictureLeft = 79; pictureTop = 1; pictureWidth = 310; pictureHeight = 310; startGroup; pictureID = 32597; ] :[font = input; preserveAspect; endGroup; ] DensityPlot[Sin[x/y], {x, -10,10}, {y,-10,10}, PlotPoints->250, Mesh->False] :[font = section; inactive; initialization; Cclosed; preserveAspect; startGroup; ] Mathematica 2.0 Initialization Cells ;[s] 2:0,1;11,0;37,-1; 2:1,19,14,New York,1,14,0,0,0;1,19,14,New York,3,14,0,0,0; :[font = subsubsection; inactive; initialization; preserveAspect; startGroup; ] Vector Drawers :[font = input; initialization; preserveAspect; startGroup; ] *) (* Two and Three Dimensional Vector Builder *) (* It includes a couple of useful commands like the cross product and norm of a vector. *) (* Bill Davis, January, 1991 *) (* :[font = input; initialization; preserveAspect; startGroup; ] *) BeginPackage["`Vectors3D`"]; Perp::usage = "Perp[expr] returns a single 3-d vector which is perpendicular to the vector, 'expr'."; Cross::usage = "Cross[a,b] returns the cross product of a and b."; Norm::usage = "Norm[expr] returns the Euclidean length of the vector, 'expr'."; Turn::usage = "Turn[expr] returns an orthogonal 3 by 3 matrix which takes {0,0,1} to 'expr'."; Vector3D::usage = "Vector3D[a,b] produces the 3-d graphics object, a vector from a to b. Vector3D[a,b,PlotStyle->{styles}] produces the graphics object with the styles included."; Vector3D::notnum = "The vectors `1` and `2` aren't numeric."; Vector2D::usage = "Vector2D[a,b] produces a 2-d graphics object, a vector from a to b. Vector[a,b,PlotStyle->{styles}] produces the graphics object with the styles included."; Begin["`Private`"] SetOptions[ParametricPlot,AspectRatio->Automatic]; SetOptions[Plot,AspectRatio->Automatic]; SetOptions[Graphics,AspectRatio->Automatic]; Z = {0,0}; (* The Origin *) (* Perp[a] returns a single vector perpendicular to a *) Perp[a_?VectorQ] := If[a[[1]]==0,Return[{1,0,0}], (*else*) If[a[[2]]==0,Return[{0,1,0}], (*else*) Return[{-a[[2]],a[[1]],0}]]]; (* Cross product of 3-dim vectors *) Cross[a_?VectorQ,b_?VectorQ]:={a[[2]]b[[3]]-a[[3]]b[[2]], a[[3]]b[[1]]-a[[1]]b[[3]], a[[1]]b[[2]]-a[[2]]b[[1]]}; (* Length of a vector *) Norm[a_?VectorQ]:=Sqrt[a.a]; (* Produce an orthogonal matrix which moves {0,0,1} to the direction of the vector a *) Turn[a_?VectorQ] := Block[{A = a, B}, B = Perp[A]/Norm[Perp[A]]; A = a/Norm[a]; Return[Transpose[{B,A~Cross~B,A}]] ]; corn = Table[N[1/4 {Cos[2 k Pi/7],Sin[2 k Pi/7],-4}],{k,0,7}]; corners[a_] := N[Table[(a.corn[[j]]),{j,1,8}]]; Vector3D[a_,b_] := Block[{A,B,AA,BB,m,aa,bb}, aa=N[a];bb=N[b]; If[!NumberQ[aa.aa+bb.bb], Message[Vector3D::notnum,a,b];Return[Null], A = Turn[bb-aa]; B = 0.13 Norm[bb-aa] corners[N[A]]; AA = Table[Line[{bb,bb+B[[m]]}],{m,1,7}]; BB = Table[bb + B[[m]],{m,1,8}]; Return[Graphics3D[Join[{Line[{aa,bb}],Line[BB]},AA]]] ]]; Vector3D[from_,to_,style___]:= Graphics3D[ Flatten[Join[{PlotStyle/.style}, Vector3D[from,to]/.Graphics3D->List],1] ]; Vector2D[from_,to_] := Block[{A,B,AA,BB,c,d}, AA=N[to]; BB=N[from]; A=AA-BB; B = RotateLeft[A] {-1,1}; c = AA - 0.1 A + .02 B; d = AA - 0.1 A - .02 B; Return[ Graphics[ Line[{BB,AA,c,d,AA}] ]]]; Vector2D[from_,to_,style___]:= Graphics[ Flatten[Join[{PlotStyle/.style}, Vector2D[from,to]/.Graphics->List],1] ]; SetOptions[ParametricPlot,AspectRatio->Automatic]; SetOptions[Plot,AspectRatio->Automatic]; SetOptions[Graphics,AspectRatio->Automatic]; Protect[Perp,Cross,Turn,Vector3D,Vector2D]; End[] EndPackage[] Null (* :[font = output; output; inactive; preserveAspect; ] "Global`Vectors3D`Private`" ;[o] Global`Vectors3D`Private` :[font = output; output; inactive; preserveAspect; endGroup; endGroup; endGroup; ] "Global`Vectors3D`Private`" ;[o] Global`Vectors3D`Private` :[font = subsubsection; inactive; initialization; Cclosed; preserveAspect; startGroup; ] Turn Off Annoying Messages :[font = input; initialization; preserveAspect; endGroup; endGroup; ] *) Off[General::spell1]; Off[ParametricPlot3D::ppcom]; (* :[font = section; inactive; Cclosed; dontPreserveAspect; startGroup; ] Animation Portfolio :[font = subsection; inactive; Cclosed; dontPreserveAspect; startGroup; ] "Fly around" 3D view of saddle ;[s] 1:0,1;31,-1; 2:0,17,12,Chicago,1,12,0,0,0;1,17,12,Chicago,0,12,0,0,0; :[font = input; preserveAspect; ] Table[Show[h, ViewPoint->{4.120, d Degree, 71 Degree}],{d,0,360,45}] :[font = input; preserveAspect; ] f[x_,y_] = y^2 - x^2 surface = Plot3D[f[x,y],{x,-6,6},{y,-7,7}, DisplayFunction->Identity] :[font = input; Cclosed; preserveAspect; startGroup; ] Table[Show[surface,DisplayFunction->$DisplayFunction, Boxed->False, Axes->None, Mesh->False, ViewPoint->{2.130, q Degree, 10 Degree}], {q,-360, 360, 90}] :[font = postscript; PICT; formatAsPICT; output; inactive; Cclosed; preserveAspect; pictureLeft = 34; pictureWidth = 280; pictureHeight = 106; startGroup; pictureID = 1385; ] :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 106; pictureID = 14438; ] :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 280; pictureHeight = 106; pictureID = 6207; ] :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 269; pictureHeight = 111; pictureID = 26367; ] :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 266; pictureHeight = 112; pictureID = 2832; ] :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 269; pictureHeight = 111; pictureID = 25636; ] :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 280; pictureHeight = 106; pictureID = 22694; ] :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 106; pictureID = 22510; ] :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 280; pictureHeight = 106; endGroup; endGroup; endGroup; pictureID = 14718; ] :[font = subsection; inactive; Cclosed; dontPreserveAspect; startGroup; ] Limiting Rectangles ;[s] 1:0,1;21,-1; 2:0,17,12,Chicago,1,12,0,0,0;1,17,12,Chicago,0,12,0,0,0; :[font = postscript; PICT; formatAsPICT; output; inactive; Cclosed; preserveAspect; pictureLeft = 34; pictureWidth = 360; pictureHeight = 136; startGroup; pictureID = 16782; animationSpeed = 0; infiniteLoop; loopDistance = 1; ] :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 360; pictureHeight = 136; pictureID = 31047; animationSpeed = 6; ] :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 360; pictureHeight = 136; pictureID = 7645; animationSpeed = 6; ] :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 360; pictureHeight = 136; pictureID = 1699; animationSpeed = 6; ] :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 360; pictureHeight = 136; pictureID = 25864; animationSpeed = 6; ] :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 360; pictureHeight = 136; pictureID = 1241; animationSpeed = 6; ] :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 360; pictureHeight = 136; pictureID = 6780; animationSpeed = 6; ] :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 360; pictureHeight = 136; pictureID = 23145; animationSpeed = 6; ] :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 360; pictureHeight = 136; pictureID = 22980; animationSpeed = 6; ] :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 360; pictureHeight = 136; pictureID = 21885; animationSpeed = 6; ] :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 360; pictureHeight = 136; pictureID = 31598; animationSpeed = 6; ] :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 360; pictureHeight = 136; pictureID = 13171; animationSpeed = 6; ] :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 360; pictureHeight = 136; pictureID = 10556; animationSpeed = 6; ] :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 360; pictureHeight = 136; endGroup; pictureID = 11656; animationSpeed = 6; infiniteLoop; loopDistance = -1; ] :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 360; pictureHeight = 136; pictureID = 13166; ] :[font = input; preserveAspect; endGroup; endGroup; ] Here's what 150 rectangles under x looks like. Notice how small the base of the rectangles are. That is, as n goes to infinity, base width goes to zero. :[font = section; inactive; Cclosed; dontPreserveAspect; startGroup; ] Area Under Curve Demo :[font = smalltext; inactive; preserveAspect; ] To better assist students visualize the concept of integral, Riemann Sums, and limit, this program enables us to alter a picture of rectangles under a curve. Default refers to # rectangles, and refers to the function being graphed. Simply change these to vary the results. Thank you, Allan, for the help here! :[font = input; Cclosed; preserveAspect; startGroup; ] Rectangle Code :[font = input; initialization; preserveAspect; startGroup; ] *) BeginPackage["RSPlot`", "Utilities`FilterOptions`"] EndPackage[] RSPlot::usage = "RSPlot[f ,{x, xmin, xmax}] generates a plot of f as a function of x from xmin to xmax, with the area b/w f and the x-axis filled with rectangles. The color, location, and number of rectangles can be given by the AreaColor, AreaLocation, AreaDivision options. RSPlot can only plot one function at a time."; AreaBorder::usage = "An options to RSPlot. AreaBorder determines the color of the border of the rectangles. This option requires only a color primitive (i.e. Hue[0], RGBColor[.5,.5,.5], etc.) If no color is given, the rectangle defaults to black (RGBColor[0,0,0])."; AreaColor::usage = "An option to RSPlot. AreaColor determines the color of the rectangles. This option requires only a color primitive (i.e. Hue[0], RGBColor[.5,.5,.5], etc.) If no color is given, the rectangle defaults to None."; AreaDivision::usage = "An option to RSPlot. AreaDivision determines the number of rectangles in an RSPlot. This option requires only a positive integer. If no integer is given, the number of rectangles defaults to 20."; AreaLocation::usage = "An option to RSPlot. AreaLocation determines the location of the rectangles in an RSPlot. The options takes either the primitive Left, Right, or Middle. If no primitive is given, the rectangle defaults to Left."; LeftPoint::usage = "An option value for the option AreaLocation for RSPlot. LeftPoint plots the rectangles using the left-hand endpoints."; RightPoint::usage = "An option value for the option AreaLocation for RSPlot. RightPoint plots the rectangles using the right-hand endpoints."; MiddlePoint::usage = "An option value for the option AreaLocation for RSPlot. MiddlePoint plots the rectangles using the middle points."; RSPlot; Protect[LeftPoint,RightPoint,MiddlePoint]; Begin["RSPlot`Private`"] (* MAKE ALTERATIONS HERE *) defaultcol = None; defaultloc = LeftPoint; defaultdiv = 10; defaultbor = RGBColor[0,0,0]; Options[RSPlot] = Join[{AreaColor -> defaultcol, AreaDivision -> defaultdiv, AreaLocation -> defaultloc, AreaBorder -> defaultbor}, Options[Plot]]; RSPlot::badbord = "The AreaBorder option has been given a bad value '`1`'; \r using '`2`' in its place."; RSPlot::badcolo = "The AreaColor option has been given a bad value '`1`'; \r using '`2`' in its place."; RSPlot::baddivi = "The AreaDivision option has been given a bad value '`1`'; \r using '`2`' in its place."; RSPlot::badloca = "The AreaLocation option has been given a bad value '`1`'; \r using '`2`' in its place."; RSPlot::badflis = "Since only one function can be RS-plotted at a time, only the first function will be used."; RSPlot[func_,{x_Symbol,xmin_,xmax_},opts___] := Module[{step,recs,lines,i,fplot,points, areadiv,areacol,arealoc,areabor,f,disp,areas = {}}, f = Evaluate[Part[Flatten[{func}],1]]; areabor = Evaluate[AreaBorder /.{opts}/.Options[RSPlot]]; areadiv = Evaluate[AreaDivision /.{opts}/.Options[RSPlot]]; areacol = Evaluate[AreaColor /.{opts}/.Options[RSPlot]]; arealoc = Evaluate[AreaLocation /.{opts}/.Options[RSPlot]]; disp = Evaluate[DisplayFunction/.{opts}/.Options[RSPlot]]; If[Length[Flatten[{func}]] > 1,Message[RSPlot::badflis]]; If[!IntegerQ[areadiv], Message[RSPlot::baddivi,areadiv,defaultdiv]; areadiv = defaultdiv]; If[!MatchQ[areacol,(RGBColor[___] | Hue[___] | CMYKColor[___] | GrayLevel[___] | None)], Message[RSPlot::badcolo,areacol,defaultcol]; areacol = defaultcol]; If[!MatchQ[areabor,(RGBColor[___] | Hue[___] | CMYKColor[___] | GrayLevel[___] | None)], Message[RSPlot::badbord,areabor,defaultbor]; areabor = defaultbor]; If[!MatchQ[arealoc,(LeftPoint | RightPoint | MiddlePoint)], Message[RSPlot::badloca,arealoc,defaultloc]; arealoc = defaultloc]; step = (xmax - xmin)/areadiv; points = Switch[arealoc, LeftPoint, Table[{{i,0},{i,f/.x->i},{i+step,f/.x->i},{i+step,0}}, {i,xmin,xmax-step,step}], RightPoint, Table[{{i-step,0},{i-step,f/.x->i}, {i,f/.x->i},{i,0}}, {i,xmin+step,xmax,step}], MiddlePoint, Table[{{i-step/2,0},{i-step/2,f/.x->i}, {i+step/2,f/.x->i},{i+step/2,0}}, {i,xmin+step,xmax,step}]]; If[areacol =!= None, AppendTo[areas, Evaluate[Table[Graphics[ {areacol,Polygon[points[[i]]]}], {i,1,Length[points]}]] ] ]; If[areabor =!= None, AppendTo[areas, Evaluate[Table[Graphics[ {areabor,Line[points[[i]]]}], {i,1,Length[points]}]] ] ]; fplot = Plot[f,{x,xmin,xmax}, DisplayFunction:>Identity, Evaluate[FilterOptions[Plot,opts]]]; Show[fplot,areas,fplot,DisplayFunction:>disp] (* End Module *) ] End[]; Null (* ;[s] 3:0,0;1901,1;1922,0;5117,-1; 2:2,14,10,Courier,1,12,0,0,0;1,15,10,Courier,1,13,65535,0,0; :[font = output; output; inactive; preserveAspect; ] "RSPlot`" ;[o] RSPlot` :[font = output; output; inactive; preserveAspect; endGroup; ] "RSPlot`Private`" ;[o] RSPlot`Private` :[font = input; preserveAspect; ] (* MAKE ALTERATIONS for function and intervals HERE *) ;[s] 3:0,0;4,1;52,0;57,-1; 2:2,14,10,Courier,1,12,0,0,0;1,15,10,Courier,1,13,65535,0,0; :[font = input; Cclosed; preserveAspect; startGroup; ] RSPlot[Cos[x],{x,0,2Pi},DisplayFunction->Identity] :[font = output; output; inactive; preserveAspect; endGroup; ] The Unformatted text for this cell was not generated. Use options in the Actions Preferences dialog box to control when Unformatted text is generated. ;[o] -Graphics- :[font = input; Cclosed; preserveAspect; startGroup; ] Show[%,DisplayFunction->$DisplayFunction]; :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 174; endGroup; pictureID = 22920; ] :[font = input; Cclosed; preserveAspect; startGroup; ] ?RSPlot :[font = info; inactive; preserveAspect; endGroup; ] RSPlot[f ,{x, xmin, xmax}] generates a plot of f as a function of x from xmin to xmax, with the area b/w f and the x-axis filled with rectangles. The color, location, and number of rectangles can be given by the AreaColor, AreaLocation, AreaDivision options. RSPlot can only plot one function at a time. :[font = input; Cclosed; preserveAspect; startGroup; ] ?AreaDivision :[font = info; inactive; preserveAspect; endGroup; endGroup; endGroup; ] An option to RSPlot. AreaDivision determines the number of rectangles in an RSPlot. This option requires only a positive integer. If no integer is given, the number of rectangles defaults to 20. :[font = section; inactive; Cclosed; dontPreserveAspect; startGroup; ] Derivitive Stuff :[font = input; preserveAspect; ] Clear[t,P,x,y] P[t_] = {t,t^3}; curveplot = ParametricPlot[P[t],{t,-2,2}, PlotStyle->Thickness[0.01], PlotRange->All]; :[font = input; Cclosed; preserveAspect; startGroup; ] Clear[vel,accel] vel[t_] = D[P[t],t] :[font = input; Cclosed; preserveAspect; startGroup; ] ??Vector2D :[font = input; preserveAspect; endGroup; ] Clear[unittan] unittan[t_] = vel[t]/Sqrt[vel[t].vel[t]]; :[font = input; Cclosed; preserveAspect; startGroup; animationSpeed = 12; ] velvectors = Show[ Table[Vector2D[P[t],(P[t] + unittan[t]),PlotStyle->{Thickness[.02],RGBColor[0,0,1]}], {t,-2,2,.5}]] :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 93; pictureHeight = 386; pictureID = 15827; ] :[font = output; output; inactive; preserveAspect; endGroup; endGroup; ] The Unformatted text for this cell was not generated. Use options in the Actions Preferences dialog box to control when Unformatted text is generated. ;[o] -Graphics- :[font = input; Cclosed; preserveAspect; startGroup; ] balls = Show[Table[Graphics[{PointSize[0.02],Point[{t,3t^2}]}],{t,-2,2,.25}]] :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 95; pictureHeight = 287; pictureID = 29410; ] :[font = output; output; inactive; preserveAspect; endGroup; ] The Unformatted text for this cell was not generated. Use options in the Actions Preferences dialog box to control when Unformatted text is generated. ;[o] -Graphics- :[font = input; Cclosed; preserveAspect; startGroup; ] velocities = Show[curveplot,velvectors,balls, AspectRatio->Automatic]; :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 176; pictureHeight = 385; endGroup; pictureID = 12920; ] :[font = smalltext; inactive; Cclosed; preserveAspect; startGroup; ] Compare the graphs of f, f', f'', and f'''. :[font = input; Cclosed; preserveAspect; startGroup; ] h[x_] = x^3 g = Plot[h[x], {x, -1.5,1.5},PlotRange->{{-1.5,1.5},{-4,4}},DisplayFunction->Identity]; g1 = Plot[h'[x], {x,-1.5,1.5},PlotRange->{{-1.5,1.5},{-4,4}},DisplayFunction->Identity]; g2 = Plot[h''[x], {x,-1.5,1.5},PlotRange->{{-1.5,1.5},{-4,4}},DisplayFunction->Identity]; g3 = Plot[h'''[x], {x,-1.5,1.5},PlotRange->{{-1.5,1.5},{-4,4}},DisplayFunction->Identity]; Show[GraphicsArray[{g, g1,g2, g3}],DisplayFunction->$DisplayFunction]; :[font = postscript; PICT; formatAsPICT; output; inactive; preserveAspect; pictureLeft = 0; pictureTop = 9; pictureWidth = 440; pictureHeight = 272; endGroup; endGroup; endGroup; pictureID = 12233; ] :[font = section; inactive; Cclosed; dontPreserveAspect; startGroup; ] Funky Fonts :[font = subsection; inactive; Cclosed; dontPreserveAspect; startGroup; ] Rabbits vs. Robots (assigning pencil vs. calculator racers) ;[s] 1:0,1;60,-1; 2:0,17,12,Chicago,1,12,0,0,0;1,17,12,Chicago,0,12,0,0,0; :[font = input; preserveAspect; endGroup; ] Rabbits (no calculators) Robots (calculators) Anglen, Donald Barrette, Shirley BonDurant, Edward Caldwell, Jenna Case, Jr. Robert Clinton, Nancy Conroy, Susan Cremer, Marcella Davis, Ronald Doenes, James Hayes, James Jones, Roberta Kang, Shinae Lagle, Gena Kenyen, Jo Lagle, Gena Luker, John Lystilla, David McLaughin, Pat Robinson, Marian Simpson, Charles Smith, Judy Smith, Kathleen Sparks, Dennis Wilkins, Jay Yu, Paul ;[s] 55:0,0;1,1;37,2;72,0;91,2;96,0;118,1;122,0;144,1;148,0;168,2;173,0;194,1;198,0;217,1;221,0;239,2;244,0;265,2;270,0;288,1;292,0;310,2;315,0;332,2;337,0;356,1;360,0;377,2;382,0;398,1;402,0;413,2;417,1;421,0;437,2;442,0;458,1;462,0;482,2;487,0;506,2;511,0;532,2;536,0;557,1;560,0;576,1;579,0;599,2;603,0;622,2;626,0;643,1;646,0;655,-1; 3:27,14,10,Courier,1,12,0,0,0;13,17,12,Geneva,0,12,65535,20578,65026;15,17,12,New York,0,12,30194,37374,54500; :[font = subsection; inactive; Cclosed; dontPreserveAspect; startGroup; ] Cards and Probability ;[s] 1:0,1;22,-1; 2:0,17,12,Chicago,1,12,0,0,0;1,17,12,Chicago,0,12,0,0,0; :[font = input; preserveAspect; ] Assume we have a normal deck of cards, with markings 1-10, J, Q, K, & A, and suits: black spade black club red heart red diamond . We could refer a Jack of spades by "J ", for example. ;[s] 11:0,0;99,1;109,0;121,1;129,0;141,2;149,0;161,2;162,0;202,1;204,0;225,-1; 3:6,14,10,Courier,1,12,0,0,0;3,19,13,Symbol,1,12,0,0,0;2,19,13,Symbol,1,12,65535,0,0; :[font = subsubsection; inactive; Cclosed; preserveAspect; startGroup; ] Examples ;[s] 2:0,1;8,0;9,-1; 2:1,17,12,Chicago,1,12,0,0,0;1,17,12,Chicago,0,12,0,0,0; :[font = input; Cclosed; preserveAspect; startGroup; ] What is the probability that, by randomly chooses ONE card from this deck, we get a: 1.) red 2.) 3.) 5 4.) A 5.) black seven of diamonds ;[s] 6:0,0;102,1;103,2;109,0;122,2;123,0;154,-1; 3:3,14,10,Courier,1,12,0,0,0;1,19,13,Symbol,1,12,0,0,0;2,19,13,Symbol,1,12,65535,0,0; :[font = smalltext; inactive; preserveAspect; endGroup; ] Answers: 1.) 1/2 2.) 1/4 3.) 1/14 4.) 1/14 * 1/4 5.) 0 ;[s] 3:0,0;40,1;46,0;71,-1; 2:2,17,12,Chicago,0,12,0,0,65535;1,19,13,Symbol,0,12,65535,0,0; :[font = input; Cclosed; preserveAspect; startGroup; ] What is the probability that, by randomly chooses TWO cards from this deck, we get: 1.) a red and a blck? 2.) 3.) K Q 4.) 7 5.) A ;[s] 14:0,0;116,1;129,0;137,2;142,0;143,2;144,0;152,1;160,2;161,1;162,0;169,2;178,0;179,1;181,-1; 3:6,14,10,Courier,1,12,0,0,0;4,19,13,Symbol,1,12,0,0,0;4,19,13,Symbol,1,12,65535,0,0; :[font = smalltext; inactive; preserveAspect; endGroup; endGroup; ] Answers: 1.) 1/2 * 1/2 2.) 1/4 * 1/4 3.) (1/14 * 1/4) * (1/14 * 1/4) 4.) (1/14 * 1/4) * (1/4) 5.) same as 4 ;[s] 3:0,0;75,1;81,0;124,-1; 2:2,17,12,Chicago,0,12,0,0,65535;1,19,13,Symbol,0,12,65535,0,0; :[font = input; preserveAspect; endGroup; ] Now pick FIVE cards and compute chances of getting: 10, J, Q, K, A 4 4 4 4 7 Use your "poker intuition" to compare your results, and see if they make sense. ;[s] 17:0,0;73,2;91,1;92,2;93,1;95,2;96,1;97,2;98,1;111,2;113,1;117,2;127,0;128,2;129,1;131,0;210,1;216,-1; 3:3,14,10,Courier,1,12,0,0,0;7,19,13,Symbol,1,12,0,0,0;7,19,13,Symbol,1,12,65535,0,0; :[font = subsection; inactive; Cclosed; dontPreserveAspect; startGroup; ] A Different Outlook on Variables ;[s] 1:0,1;34,-1; 2:0,17,12,Chicago,1,12,0,0,0;1,17,12,Chicago,0,12,0,0,0; :[font = text; inactive; dontPreserveAspect; endGroup; endGroup; ] Instead of using conventional notations for unknowns (x, y, and z), it is recommended to try also some unfamiliar notations to provide a more concrete representation of word problems. Consider examples: 3 + 4 = 7 they'll see the "light" better this way than with x! 6 + 2 + + 8 + 10 collect like terms 5 + 5 = 5( + ) add apples and oranges ;[s] 32:0,0;213,1;214,0;219,1;220,0;225,1;236,5;289,6;290,0;291,7;293,0;294,7;295,0;296,7;297,0;300,7;303,0;306,7;309,0;313,7;316,5;336,0;337,2;338,0;343,3;344,0;351,2;354,4;355,0;356,3;357,0;364,5;387,-1; 8:14,17,12,Chicago,0,12,0,0,0;3,17,12,Monaco,0,12,65535,0,0;2,14,9,Helvetica,0,12,65535,0,0;2,17,12,Geneva,0,12,62517,42802,7353;1,14,9,Helvetica,0,12,0,0,0;3,16,11,Chicago,0,11,0,0,0;1,16,11,Chicago,0,11,0,65535,0;6,16,11,Geneva,0,11,5434,40528,5138; ^*)