(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 4.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 7709, 214]*) (*NotebookOutlinePosition[ 44730, 1453]*) (* CellTagsIndexPosition[ 44686, 1449]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Sample of Shooting Algorithm, for use with Lab #5", "Section", FontSize->24], Cell["Set up the right-hand side for a widget-manufacturing ODE:", "Text", FontSize->19], Cell[TextData[{ "y ' = v\nv ' = ", Cell[BoxData[ \(TraditionalForm\`125\)]], "- ", Cell[BoxData[ \(TraditionalForm\`\(3\ \@y\)\/40\)]] }], "Text", TextAlignment->Center, FontSize->24], Cell[BoxData[ RowBox[{ StyleBox[\( (*\ Obviously\ you\ need\ to\ define\ your\ own\ differential\ \ equations\ here\ *) \), FontColor->RGBColor[1, 0, 0]], "\[IndentingNewLine]", \(Clear[x, t]; f[t_, x_]\ := \ {x[\([2]\)], 125 - \(3\ \@x[\([1]\)]\)\/40}\)}]], "Input"], Cell["\<\ Define a function finalprod[v0_] which, given an initial value v0 \ for v, runs Runge-Kutta with y(0)=0, v(0)=v0, and then outputs the value of y \ at t=200.\ \>", "Text", FontSize->19], Cell[BoxData[ RowBox[{ RowBox[{\(yfinal[v0_]\), " ", ":=", "\[IndentingNewLine]", RowBox[{"Block", "[", RowBox[{\({h, ti, tf, nsteps, x, t, k1, k2, k3, k4}\), ",", "\[IndentingNewLine]", StyleBox[\( (*\ Remember\ to\ set\ h, \ ti, \ tf, \ and\ initial\ values\ of\ x\ and\ t\ \ \(\(appropriately!!\)!!\)\ *) \), FontColor->RGBColor[1, 0, 0]], "\[IndentingNewLine]", \(h = 0.2; ti = 0; tf = 200; nsteps = \((tf - ti)\)/h; x = {0, v0}; t = 0; \[IndentingNewLine]Do[\[IndentingNewLine]k1 = h*f[t, x]; \[IndentingNewLine]k2 = h*f[t + h/2, x + k1/2]; \[IndentingNewLine]k3 = h*f[t + h/2, x + k2/2]; \[IndentingNewLine]k4 = h*f[t + h, x + k3]; \[IndentingNewLine]x = x + \((k1 + 2*k2 + 2*k3 + k4)\)/6; \[IndentingNewLine]t = t + h, \[IndentingNewLine]{j, 1, nsteps}]; \[IndentingNewLine]x[\([1]\)]\)}], "\[IndentingNewLine]", "]"}]}], "\[IndentingNewLine]"}]], "Input"], Cell["\<\ Our goal is to find the value of v0 for which yfinal[v0] = 2000000, \ since the problem says we must produce 2000000 widgets after 200 days. 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If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. *******************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1776, 53, 84, 1, 72, "Section"], Cell[1863, 56, 90, 1, 35, "Text"], Cell[1956, 59, 207, 9, 85, "Text"], Cell[2166, 70, 315, 7, 89, "Input"], Cell[2484, 79, 197, 5, 60, "Text"], Cell[2684, 86, 1143, 22, 330, "Input"], Cell[3830, 110, 244, 5, 85, "Text"], Cell[4077, 117, 46, 1, 50, "Input"], Cell[4126, 120, 127, 4, 35, "Text"], Cell[4256, 126, 292, 6, 90, "Input"], Cell[4551, 134, 1214, 26, 308, "Input"], Cell[5768, 162, 177, 4, 60, "Text"], Cell[5948, 168, 1401, 31, 330, "Input"], Cell[7352, 201, 85, 1, 35, "Text"], Cell[7440, 204, 227, 5, 70, "Input"], Cell[7670, 211, 23, 0, 58, "Subsubtitle"] }, Open ]] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************)