(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 28154, 559] NotebookOptionsPosition[ 11300, 258] NotebookOutlinePosition[ 28240, 561] CellTagsIndexPosition[ 28197, 558] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`A$$ = 15, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[""], Manipulate`Dump`ThisIsNotAControl}, { Hold[""], Manipulate`Dump`ThisIsNotAControl}, { Hold[""], Manipulate`Dump`ThisIsNotAControl}, { Hold[""], Manipulate`Dump`ThisIsNotAControl}, { Hold[""], Manipulate`Dump`ThisIsNotAControl}, { Hold[""], Manipulate`Dump`ThisIsNotAControl}, { Hold[""], Manipulate`Dump`ThisIsNotAControl}, { Hold[""], Manipulate`Dump`ThisIsNotAControl}, { Hold[ Row[{ Spacer[80], Style["Range", 20]}]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`A$$], 15, ""}, 1, 100, 1}, { Hold[ Dynamic[ Column[{ Row[{ Style[-$CellContext`A$$, 20], Style[" \[LessEqual] X,Y \[LessEqual] ", 20], Style[$CellContext`A$$, 20]}], Null, Null, Null, Style[" Surface", 20], Null, Style[" z=yCos[x]+xSin[y]", 20], Null, Null, Null, Null, Framed[ Column[{ Row[{ Style["Minimum = ", 20, Blue], Style[ Round[$CellContext`mz, 0.01], 20, Blue]}], Null, Row[{ Style["at X = ", 20, Blue], Style[ Round[$CellContext`mx, 0.01], 20, Blue], Style[", Y = ", 20, Blue], Style[ Round[$CellContext`my, 0.01], 20, Blue]}], Null, If[ Or[Abs[ Round[$CellContext`mx, 0.01]] == $CellContext`A$$, Abs[ Round[$CellContext`my, 0.01]] == $CellContext`A$$], If[ And[Abs[ Round[$CellContext`mx, 0.01]] == $CellContext`A$$, Abs[ Round[$CellContext`my, 0.01]] == $CellContext`A$$], Style["Boundary Endpoint", 20, Blue], Style["Boundary Critical Point", 20, Blue]], Style["Interior Critical Point", 20, Blue]]}, Center]], Null, Null, Null, Null, Null, Framed[ Column[{ Row[{ Style["Maximum = ", 20, Red], Style[ Round[$CellContext`Mz, 0.01], 20, Red]}], Null, Row[{ Style["at X = ", 20, Red], Style[ Round[$CellContext`Mx, 0.01], 20, Red], Style[", Y = ", 20, Red], Style[ Round[$CellContext`My, 0.01], 20, Red]}], Null, If[ Or[Abs[ Round[$CellContext`Mx, 0.01]] == $CellContext`A$$, Abs[ Round[$CellContext`My, 0.01]] == $CellContext`A$$], If[ And[Abs[ Round[$CellContext`Mx, 0.01]] == $CellContext`A$$, Abs[ Round[$CellContext`My, 0.01]] == $CellContext`A$$], Style["Boundary Endpoint", 20, Red], Style["Boundary Critical Point", 20, Red]], Style["Interior Critical Point", 20, Red]]}, Center]]}, Center]]], Manipulate`Dump`ThisIsNotAControl}}, Typeset`size$$ = { 710., {253., 258.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`A$162052$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`A$$ = 15}, "ControllerVariables" :> { Hold[$CellContext`A$$, $CellContext`A$162052$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Framed[ Pane[$CellContext`M = NMaximize[{ $CellContext`f[$CellContext`x, $CellContext`y], And[-$CellContext`A$$ <= $CellContext`x <= $CellContext`A$$, \ -$CellContext`A$$ <= $CellContext`y <= $CellContext`A$$]}, {$CellContext`x, \ $CellContext`y}]; $CellContext`Mx = Part[ Part[ Part[$CellContext`M, 2], 1], 2]; $CellContext`My = Part[ Part[ Part[$CellContext`M, 2], 2], 2]; $CellContext`Mz = Part[$CellContext`M, 1]; $CellContext`m = NMinimize[{ $CellContext`f[$CellContext`x, $CellContext`y], And[-$CellContext`A$$ <= $CellContext`x <= $CellContext`A$$, \ -$CellContext`A$$ <= $CellContext`y <= $CellContext`A$$]}, {$CellContext`x, \ $CellContext`y}]; $CellContext`mx = Part[ Part[ Part[$CellContext`m, 2], 1], 2]; $CellContext`my = Part[ Part[ Part[$CellContext`m, 2], 2], 2]; $CellContext`mz = Part[$CellContext`m, 1]; Show[ Plot3D[ $CellContext`f[$CellContext`x, $CellContext`y], {$CellContext`x, \ -$CellContext`A$$, $CellContext`A$$}, {$CellContext`y, -$CellContext`A$$, \ $CellContext`A$$}], Graphics3D[{ RGBColor[1, 0, 0], PointSize[0.02], Point[{$CellContext`Mx, $CellContext`My, $CellContext`f[$CellContext`Mx, $CellContext`My]}]}], Graphics3D[{ RGBColor[0, 0, 1], PointSize[0.02], Point[{$CellContext`mx, $CellContext`my, $CellContext`f[$CellContext`mx, $CellContext`my]}]}], ImageSize -> {600, 490}, PlotRange -> {{-$CellContext`A$$, $CellContext`A$$}, \ {-$CellContext`A$$, $CellContext`A$$}, {(-2) $CellContext`A$$, 2 $CellContext`A$$}}], ImageSize -> {700, 500}, Alignment -> {Center, Center}]], "Specifications" :> {"", "", "", "", "", "", "", "", Row[{ Spacer[80], Style["Range", 20]}], {{$CellContext`A$$, 15, ""}, 1, 100, 1, Appearance -> Small}, Dynamic[ Column[{ Row[{ Style[-$CellContext`A$$, 20], Style[" \[LessEqual] X,Y \[LessEqual] ", 20], Style[$CellContext`A$$, 20]}], Null, Null, Null, Style[" Surface", 20], Null, Style[" z=yCos[x]+xSin[y]", 20], Null, Null, Null, Null, Framed[ Column[{ Row[{ Style["Minimum = ", 20, Blue], Style[ Round[$CellContext`mz, 0.01], 20, Blue]}], Null, Row[{ Style["at X = ", 20, Blue], Style[ Round[$CellContext`mx, 0.01], 20, Blue], Style[", Y = ", 20, Blue], Style[ Round[$CellContext`my, 0.01], 20, Blue]}], Null, If[ Or[Abs[ Round[$CellContext`mx, 0.01]] == $CellContext`A$$, Abs[ Round[$CellContext`my, 0.01]] == $CellContext`A$$], If[ And[Abs[ Round[$CellContext`mx, 0.01]] == $CellContext`A$$, Abs[ Round[$CellContext`my, 0.01]] == $CellContext`A$$], Style["Boundary Endpoint", 20, Blue], Style["Boundary Critical Point", 20, Blue]], Style["Interior Critical Point", 20, Blue]]}, Center]], Null, Null, Null, Null, Null, Framed[ Column[{ Row[{ Style["Maximum = ", 20, Red], Style[ Round[$CellContext`Mz, 0.01], 20, Red]}], Null, Row[{ Style["at X = ", 20, Red], Style[ Round[$CellContext`Mx, 0.01], 20, Red], Style[", Y = ", 20, Red], Style[ Round[$CellContext`My, 0.01], 20, Red]}], Null, If[ Or[Abs[ Round[$CellContext`Mx, 0.01]] == $CellContext`A$$, Abs[ Round[$CellContext`My, 0.01]] == $CellContext`A$$], If[ And[Abs[ Round[$CellContext`Mx, 0.01]] == $CellContext`A$$, Abs[ Round[$CellContext`My, 0.01]] == $CellContext`A$$], Style["Boundary Endpoint", 20, Red], Style["Boundary Critical Point", 20, Red]], Style["Interior Critical Point", 20, Red]]}, Center]]}, Center]]}, "Options" :> { ControlPlacement -> Left, FrameLabel -> { "\!\(\*\nStyleBox[\"\[Copyright]\",\nFontSize->14]\)\!\(\*\n\ StyleBox[\" \",\nFontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"N\",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\".\",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\" \",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"Bykov\",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\",\",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\" \",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"SJ\",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\" \",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"Delta\",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\" \",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"College\",\n\ FontColor->RGBColor[0, 0, 1]]\)"}}, "DefaultOptions" :> {}], ImageSizeCache->{984., {309., 314.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({{$CellContext`M = { 26.778311110051725`, {$CellContext`x -> 12.63655103040128, $CellContext`y -> 14.216189875634804`}}, $CellContext`f[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`y, Blank[]]] := $CellContext`y Cos[$CellContext`x] + $CellContext`x Sin[$CellContext`y], $CellContext`Mx = 12.63655103040128, $CellContext`My = 14.216189875634804`, $CellContext`Mz = 26.778311110051725`, $CellContext`m = {-8.104988779083138, \ {$CellContext`x -> 3.3334681130338395`, $CellContext`y -> 5.011303031741619}}, $CellContext`mx = 3.3334681130338395`, $CellContext`my = 5.011303031741619, $CellContext`mz = -8.104988779083138}; {Null}}; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{3.46998965315625*^9}] }, WindowSize->{1272, 922}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, DockedCells->FEPrivate`If[ FEPrivate`SameQ[FEPrivate`$ProductIDName, "MathematicaPlayer"], FEPrivate`Join[{ Cell[ BoxData[ GraphicsBox[ RasterBox[CompressedData[" 1:eJztXXdYVNe2z/feP/e+991rcl+aBRQpgjSlWbBrsBtbYr0xMSYWjCYaWyzB GDWmWrB3BAvSBOm9Db0zQxlmaEoVMWgUHWbm7Zk1s9mcM3MYYJDEu3/f0e+U vddee50z63fW2nsfjFZvXrj6v1977TUL9G/df732mmJf1EMIhWnTZ2YYDElY uLgoJgbOidVI/nqnxGhYwxCzGquxstEfSMevkI1bJp30UcOlG5WFArTdC49+ 5Lr9hd0kuYVD2zDbRwOH3jtzrqcqUVBQUFBQ/ImRdflKhoFRqsGQdONheR8u E1y/IcrOFuXlpR4/yTOxkw8xkQ4e+tRmknT2FunCvdLF+2Tzd8tcvng+f/Pz 2Z+1OS5os3mvzdL5ubXzM2PbhkEmlRGRfd0hCgoKCgqKXgEElYLk5HxTc4GB UZ6hUb7B0FxDk1zbMbmjXUItJvOtxsmNBssHD2kzsWpdcUSy/kLb+vOSz92l nxyXLj0kmfeNxOULyeilL0bOeGY1rs5weK25XVlael93i4KCgoKColcAvFlW UpI5ZlzRoCGFg40Lhwzjm9jmmI3JGzEvesyyxuEOCt40NmkzHvp44iLxjmuV 2y/d336l6etLTzedbfvcXbLsoGTGZonzkpbhE6sMbapGjhXl5vZ1tygoKCgo KPQPPIiJ9nNWrxENHFJhbJlrPiJ1qgtvzoLERSuiF6/gu0wqem+SYMY0wZxZ /MnOyas+i924LX7DFt7GrzM3bstbv5X/6ZeClesKF6/Imvl+hoVTkcPEsvz8 vu4ZBQUFBQWFniEmoDjc51ZtYJZrO6rk1IF7vmerfS9U+l+p8rtU63269vbp Wt+ztX7na33O1tw+UxV0rTLYs+quZ/Vdz3vBnveDrtXc8bjvd/me/wWx1/HI sRMEicncTZcVF2f6+AqTOylGQUFBQUHxJwHiynI1VMT5zb6qoQ7ZX3xW43e5 PiCoNiS2KiK5JTj0jzuBj4NCWkIjWyKiWiKjWoKCmsPC67Ny63PyGzJzGtKz G3mZD2N5qHy1X3BVUHCh++nQJaszA++WCYVkiyUCQUZsbNjRoyGfrklfurzq 1JnywsI+6j3Ffy6Ed+4IPTz6WgsKCoq/DHCACYxZoYSCOkWi4gUrqmym5327 rSbIrzE2qyYxpz46iX/6dFNE7NO0vCepuU9Ssx+n5zxOTn8cE9+SxGsuLGkq EjUWCBvT8mtjM8rDk8tCEspjUsoCowKGjr76zpBzdk7es+ZdWbj455mztjuP 3Wo+7Lc33wp6p/+9lauqEhP72hIU/4lApMl/7TW0CQwM0H4vtZJMEykUf3G4 uroGBwf3tRZ6wKlTp1BfLl261BMhJG8ixqxUQlxSkvft9yWW04STVmW57awM u1udlFMfl9Icm3Bn1NiEMRP4F680ZeU/yi5ozsxrzsxt5qWjS81R0U0JiQ8S EuuiYivDYsoCI4oDw0sjYvl3gr97d8D2fm/82u/tfX//x5d/+5+j/+wX+tbb 9f0N24aPqLvQI/0pKHqIkrVri5cuVVBnv35lcXF6l5+VlYV+qnoXS0HxMoG4 xtfXt6+10AOio6NRR1B30I7utQTJvISrV+OvXcuOjS3Oy0NxZZlQWMrnF6en F0ZG8n39c4+7p81dkmY6LnX04pRZrhluO8rv+tVFxP0eGfcgOT1+5pz7BuY5 A03iliwX+AfWZuY1ZOTW8dLrE1IaouMaQkJr7gRU+fuKfLyLb17P87yWH+CX euvGF++8e3LAMM93DLzfGVA6xEhmaiY3Mmqzta8Outtr5qGg6AIQeyLqLHJ2 1rtkypsUrwBeGd4EHD58+LffftO9vFggqL7ll77ko5PGpvsHvPubvZ27k5Of g2OSvVPqSMd0hzH8UeOLbR2F1s4VdlPqHSbl7tpYfdujMSSiMTbpfnJa5IzZ ZSY25ZaOJUaWCcbDYzd9KQgOr+RlVMbxqqLiqkLDq/wDxD4+xTdvFHp5Zl29 nOXjzb95K9t2YpWls2TkRJnVaJnFCLnxsDbbEdXh4b1nFgShh4e+xq3KsrMV 0notj0fR50CRJiRs9T7WSXmT4hXAK8abqC9btmzpRsWquETxF19lWdommwwL NxuWbjOiZcwE+Shnue1IuZmp3Hiw3GSofNjwrB2u4lvX7odGV0UnihKSQ6bP LjSzLbRy5Fs5FVs6Zg+xCBnpFH/wB0FYdFlUgjA4rNTHv+TGrQIvzxyPKymX LvBv324Ii5et2i+dt0k6fqnMcYbMwlFqaX8/IEB3VRFtgU9DG9rH5wX9+mn0 dRA74A0d4ksooCDDCsYhgqrK9u34TOnBg7ghVBJdwlVgn6/+sCFSg6EPWxop ViHHyopsWpEqVHcQkodYedwpdB45eaQA2jCVox2BgQEep4O6WDgmhdITJ7BJ URnoF6pSPGsW6AxaYTuzK0IroBUqAwZEclAfkQTQim060IShFaiNmlbZ1soK DNVeC3XQwwO1hXbQSbYNSWUYYGhO2geJQpviVnasiG9xBzlaDMW2jDZw8yZ7 2IjP56NfNDqPz3h5ee3atQudQf+jfbIwDNag8qgWOkSi3NzcXJVAO5CJgibQ 2zWUZIzscAjXeAmJInWDlBfbozKK6dIixwgaSMP9Ql1AVtUmluwjQybHYXJy MopBoAm0g4ekGVVwv5BtsanJ8qgA3D6wCaM6UhtaQWXQvUNC0D6+d9oqdlU3 jdbTaFjUNDwYCGiHLMm2FbJwl54i0kSos9BNMAKSA51F5ZEodAn1C86AcFyY rTAShUuSYrkNovFSl1K1JMSJSeJP1jwc6fjIcUzLuEmtDmNlRibyIQZyMzOZ 9Ui5lVPajo3FN66JQ6KEEbHFMfE+LjMSTW1SrBx4yi3F2jHFwi7YwOT2lGkJ x9wL7wQX+fnzPT1zr1xJv3iBd/5saXhsVVzqi+2npJ8cls7eKB27QG41vvHY 6S4pifmIpCSSTEliwvyCdsh9uNoN3sSeH51sd/I95k08IwUTJaOwiqCVLIPp DB2iptkvDFgxoDBcvr0XQDFq4dBx6AgIRBJEmsIuRkUV9ym7D/sqIVZWWCuG 6UArBQN2NBdqq/2FRNkvtGEFULugGJTRaEPotbbkKqm5ijT79VPINDDAvMy+ HYzXMG2GYltGGzrlTQbpILcDroY8RJ4EFUP/g/uCS+B10SG6hLwHuALkkXyV QDtQEjwMnEdnSKfHIVzbJSBKUgGNUyzIYuzeaWyRI6LB7AxdABdNFgaxyM5Q ADlhjTK1HaJ7hMyCakET4MOBmhlVcL+QtaE5BMQO+NUF6QZygN3I6vBGhAqT rWAraavYDd10vBcIwF/wCGEu02Yr/HTBU9Tpo4JNBOXhVwBGAHqFS8gg6Dz6 H84gCbgwA6guqogVBrHoDKZODoMwLsELQE9mB4nF4spj7s/GT5GOniBxmiyx nigdaiw3MpTZOMpGvcfb5lroeaUkKIwfHFEQFnll6rQbRuY+5ra3ic3XwvaW kfm5gYOvL1yccvZcvqdXzsVLCWdOZ3ndKIiML4lKbN5zVrrxuHTJXtmEFa0L 1og6LkjpFNjfkm6KJFPsyjCZMtgH01NXeRO3gtkNeXi98Ca+CoXbJ3aqZ6dg abgh5KhVDakLM3gQSFaRVVYXYBArqM2+Cs3BDoOnGNxEdhkaRezJuMTsvjo4 ZbSLy+O2IB+uMrjSCOgM0JNGcmTYnwFSc1VsqA5a8WsG2X0wPtkWt6G4WRuj S7yJXSv+vZMOSqT0UTi/xPCH7CgAN4F5hCGBQ7i2S7hR8OfaBom0+WqOFjvl TfIM+GccLzDEkn3XhTfRDULul6yIDuGu6cJN6K7hcIajRXixIeMjiCJ7VTeO 8yKW3bj16cZTxD6JbhzJdBqhUYJIzfJkqoHxEOrOm0C4QNndRkVFxb2wcMl7 c+TW49pGL5ZM3yCxGyMzNJDZjk7ctiHH42Kh393cgOCcoJCTkyb/MsjohLH5 8Y4bOuNubP5Lf8MjhkY3V6+OOXYs7fz5zMCwnNDowvDY+27nXmw7Kf34oGzS x3W3upChBagclJKwGF5alSdUE0rpiROk1xWx8mld5k1WVKivPC1uHa6Sfhv3 EUtjqwGxHn5hUBFrv37aOkIWIBlZm1baJLf38c4dMiIGaIxqsSiGVtpYD4yA 858QO5Ndw2AbnASpOTxCOO3QHlarE92qtLkyqGx/meE0FNvmGtEl3gSPgX/v KPRAOwxHgc5ASEK6BXZJbU1gCRzCOS5Bo/DmTzpSBjT6au7udIk3RcoIBQhF 975rO4RsIVkR3Du7ikZNIO7GWXHdeZPDsetLN47z3BK4TafLo0I2BMlVkfKu dRrl4cIkQCy7LrxBdRqAk5fgfsHt0PjY6Ijy8vLKysqa+MS2CXNlTh9IF33z YN3RlvEz5UNNeds2FN64WnI3vDAkvCA08syUqccNTU6bDte4nTGzPGVs8etb A8/b2MZ8fyAnLEoQm1QclVjpdvbxtpOy1QelM9ZXx3V5LRt4Y8aAoGr4D4eT SqLU6IpJX92NPK2Kr2fNAh+rR96ENDLQCtTFfhu6A01DdTw4qBqIVL4hYKfN fmFgcBbJd3gfSWZsInZs2zEAJDulGN9Uv8yojEP0CB9iUaKOIao23sREiTqF msA5BI3zsjgs3KHLd+7gOJptW6wM0hwsqQrMOQ1Fytd4fwG68yYEm5CDgt+7 Ro+Hq5BXyUwmBo6AGOM44DQ4hHd6CTEmd9SgUQJ3d7rKm3iISmPfNTpSbYfs pnGL3NyE2AEyftpCHsb9hZcNpDOYThee6rZunZ7nlsDWp6tPEeyjWhDG4u7g /DbjZiGb4CQ8e6QbGmIvhQbi1mgrbd1BCkCkCe+oGi2jC4A3UdRZ5x8os58n XbCr2fV4wdYTTWOnZu5wFfp4lUfElkbGFUfHXXeZEWhqHWJlr2GztA82HxFm Y5e6cHbSTtfoM6eKo+LEvIzypLQqtzMPd5xoW/eTfPrm+sveXdINu028A+fB 7ynmoih3IDzpDd6EmSF8YqKRvnhTxX1KWgGyUBCQUggwiyqoJEJseIUgN5zP 5HecpsLmLD6Rq2QIaZdGZkphahBLMhn4k9Nm8KYh/MfROqEVm+tJy0Ar5KZx ahBOmwOdAdXiG0dWJOcg4a3dtkrFyMFQuIkchmLI1wbdeZOdC+0qb7Ih0uLx dCFHjktsmQy8BN6EAAS/ZjCgUaZ+uQkmZcF4ZadNYJ3xDB/yHuldt06tp7HR rvIm96MiUpuIMZdJ481CwmF0FVXRGANCXMl+VYMkOcShOnYHT15CbzscORNu iMXiCjXQ/tNVW2SzNj91PSrcdirvq58zv/lC7OtVHRUvjk0qjU/2mzEz2dQm 3doxzUq5qXdSLezTh9sVuEzJ37Eu5tSvuSFhlZl5FUmplbz0Kl7Gve/OPth2 TLL2iGze1xKXNZVpXQiNVQlMpaclc2iYsHDgKdJfnha70w6aKCM1cmJMD3kT 64Z2QBRJ7uikKvIiuE+EF8V4eKjCcMZMV3VbGiJQiLCUuUrGZN32mM7DQxtR Mmb2kulZ6AuqyyBK9iwjcr6uYuxS+5wfbFKFzTtmWUmwX2kUgaqayBiaq2Qq 7yMjyUzmzHHOlttQoo6D3dqgI2/iYFNE/N51z9OSMzMB6KrGbB5IQOV7kqdF DkeXeJOMKVBh/eZpRerghd13Vx2ypuRhN3Kh0ChbYe4WAWAKJAG4QO+6MUC+ V8BoIMliuvNmV58inA4llWFP2wY5EIlzPFFAwRovwWOgY3dAYfYvqKvAHwsC 3ny054hs2ucvPvupZqt77p6zGQd2VPtdr41JrE5IESWmhE6fXWRiW2zpWGzp oPzfsdjCvth8ZPk4Z7HryhT3I/FeXpnet2szsusyc+tSMmrTsmp5mbV73R/t PCn5eL90/jb56CWtC9ZVZOXoqF6HvKg6KFBlNZVOjyygr3lBMP8TziDnTwZE 4MMZmUZw1JgUVLEYpmzt8QgeyyN5E4ecjGFNhSbkMhzGTNeO01Rw6zhrSjp5 uIqXvTDoQDUVx8pKZTRlRYVNiGRs+9sCkaXUMB23IzNqnBqEJZMgz5DvKgyQ twC/1WDSZ1QkZTKmHJO8idVWvEVwGgo3x0H9OvKmtgk/XZoXxJjjAclDV9aM DswyPZkXxE2d7BgQiIx7XlBXZxm5qhc4kGJJGiX7DoEJbgIOQSvuuTca58No W9zBphuyUwxzwdxRbRVxyNZV3Rgg32EgEYqKaXxXYRANqXk3niKNJmJ0B4/5 dpoy1ZE3tRkE95S0OfkMdAnkR/YUX6YtFba+/7F0ymrpxwcfbT1ZvOtU5uE9 NYG3mmIS6pPSqnlpUTNmlxvblA93UGwW9uVmI6pHOtasnJ/3q1uqj3dhYHB+ 4N1C/4D69OwHmXlNKVnNGTnNKZnNmw61bPpZsspNOnODbMJKubXL85nLq+Li ddGQHQggZ4V3RMSMGiiv4zoUWMGnWpenXJ5AJjBxOhTiHWAfch0KFMZOW7XA QS1NcWhlhYVwfL0N947kTRERcpJeGhZuMDTBg5J4xQQegGvXx8AApz0xjeLx YiwN2xAfkhVV/VK30j60evCgYmHj0qUKHdSFEUNBEI1XTcLqGJGW+bqKfoEE 5VIUkZK7VdlXvHCVmF+EgWN8HB2rBCqDdEZCADWh6C96MJBiauPAJY2vW0C4 HIbCY8HshS0YuvAmw/OT7ot7kj/2h7gWDB7BJRxzuXZcQaCvdSgco5zamI57 HQoEHeyZsRqlkQk6vDIComxyHQpegwMrOCB8w4egPPdaD8YqHnI9Ba6CLuFg HG4BJiayU+gS7JP3QltFXx3WoWjUjdt6WHNRZ7xJas5uq9OnCBrCVeBphO5A chvkADvDXCBsGTaX6Zin1WYQ3FPUNPk+gA678VkSxnfda/2DpNaT2iYslS7Z 17rx2L0d7jk/7qsP8f09OvZhUlpdWmb0TBVvis1GVljZ1c6fXnJgS8p1D0F0 3P3E5PuRUQV3gvL8/RvScxozch/wMpuz8h+n5jz5dM8fy7bLPtglnfqJbPRC mcM8ucMsifOMsktXOtWQnF0J0Qq4PtLLMegJXSVXDmr87gG5toX0mdgJ4/FT xUcGOo61tWcsiWAHtwjL6vEh9/o+7J9BMez8ccjJiIMYI3QKliFCQnJDtsJT gzD1kHG0SJnLJQ2F42Kcw+zQrxMnOvSLmJuq0T7kAluSatmTbBnjtvidhBw2 5fjuOkMfnCsmZ0DhyVRkQ2SXGeTLiCu1GQq/s+F5R2z1dOFN+I1jn8BwdBoX lcMZDHCkwBpQEvtD166vWOe4ROoGy9XRVfaAFEcGTKNY/OYPeuoijZEGBBvC GwJYEi8PgSFF1ByqgkcY4RBL0/htAYZWjIX25EcMYLUseUfQIbtT8DCQC/xF xIpdXFGknnXTbd24rQcLOhitiIgIka25a7e+noFUhUVVqApuiPHxB6wzRIIg pBvzgrgNAmUgh0wKB83ZRuMGyZuVfMGz6fOlVuMko+e8mLW+deX+B66/5P2w tyHE53Fk1KOE5AepGSEzZ+cPteJb2ImmThRu+yz98umcoBBxdHxdYnJdfHxt RETp3aAcP7+6pLT6lKyGpPSmjLxHqTkP/r3ryYLNzyavaRuzTGI/T2o9VWYz UW47WTZifNP6Lyt4KdrUY68XwHzBJ5OB6gm3ZF2N39nrNE/LkNCuiXpUUauq ygLkpBTgXG3lAXhaLKNHIoJf2KEWMAIpvMMs2bVrQRNyoQSMP5JpXrKbnfeL bEtLv0AO2QT5rQPIo2JNNCZm2RpqK0yCcRMZXMl+e2HfSnymg/JsI7MMRYpi PAAYnfImYxW5SOdhFx2LuWofN+wG9KtbTxoF98i9EvDlo9vW1u9tIqGRN/V4 d14OdFmHwgG9mxdT56NPP28bbvfcekyb/TSJ8+Lnczc1LN+bfWBXbeDNR2Fh D6NiGuMTvKe5xNmMKPh8WcbJH7P8/UUR0dUxsaKIqPLwiJrw8Mq7d0sDAjJu e9+PjL0fy6uKTKrlZTXxch6t+f7J4u2tUz995jhHYvOe1NpFNny83NxJbj5K sWLUdlzjR2vKff1EJSUM3XDsgM/gPCF5kmPeCANd4s2XgPbP46gH1PAl3Hcy McgNxhJX9hKSlw/2pFONJNUTMMZb8ZijaupOx48zvHx0ypvk12YAOpIOx/fT GE28erwJMZrGbx30Lf78vEnmaf9a6PS7BxzoJfOWrF0vGWousbB7YmrTOMyx znpK1ZilubPWp+3fUelztT7Arz4wsCY4JGDOjMRvNqV5XS3yDxSFhAqDQ4uC ggsDg3IDAvL9/Apv3869eSPx2tWygBBhRGJpaHxFXFpDfMazVd8/m7Op1WGh xPK9Z47TH63c8HD3gYaj7vXnLtZdvNrgfrZ593cPt+ysPc50L+Qwk1pPlZMk 53Oyi2mDRt5kTFh9ySAzh4xwhrykC/fBxBj215M6/YZqrwIxJozJMrTizmB3 ST4jIUw+Hhpn/75MdMqbbP+vO+noMqWhD3nTl0BP/ggpY2YLpP56+CcUewlZ SvS8oqt6rkvPodF63f40ax+i0+/scUD/8Saf3+C6WTLIqHWQUZOBcY2hiXio ZcXwsXy7mRkz1vK+/Vroda78uqf45s3ymzd5v/yUe80z/5Z3gbe30MdX6Oub f/Nm0rVrcVevoi358uWUixcjzp4p8LwlCIwW+EVUxqQ0JmY+n79FMmZpy+J1 DcfPVaRlaFVFWMY4gVwink+iKqJM/TFOwhQUXfwwgzdxFhH51b4KSeC75aqv s3YMwRTDrOpL3ftrLDp+Q/UlA7TSl8FhJJfc4JsMcJXxpfqXj055kxFsinQO JHVEn/Am+SV2je8GXQLju+7Inq/8nwLXI2+S1oPo7K9ImgDu77pzQL+/glrP my+cp7QMMqoYZlUx0rHUzlHkMIpvapltYJ5mNjpx8vKo9Z/xb1wqvu5V7H2r 5La3wOd2mb+/OCKyMiW9OjuvKiPnXlJKZXhUqZ8f77pXxOVLEZcuhl48n3LV ozQoShQa97Cssio44sXY5X8sWicWFOlL7W4DSIrM6OJJRH0YkvQe2P39MwCG Dl/O32XDrNpXfwauz/+OmKv2vzPSDeiX0ykoXg709SsQ5+cL3c8Efbzad9eu bF+/0owMYUGBqLBQlJ9fGheXe/JU3PvLAu1n+o8ax/vlR1F6Wm1paaNY3FhV 3Vhb96C+salBudXVP6ypa66pfXCvpqHyXl2ZqKKkpFQgKCsSNIrLHz981FRR kT9l4VOLyTXXb/dcZwqKvxz6nDcpKCj0hbLCwrz0dPZ5PE2oODMz0HGal7HJ dXOz4GnTcletLdhxKHX3Yd6ugyl7DmbuP4K29H2Hsnd8K9jyTdrGHfFrvor+ bFvE6q03Zs/fO945bMas7PnLC+2nNtpMfGxiXx149+X3kYKizwF/bbCvtaCg oOhdYOr0meLy65v/OjZgiNBxunTt0Rd7rtR+f0140EN46KroR0/xT9dEP3pU 7j/3x+bDorUHslfuSV71XdKyb/MWbfcwd1r7xuulZlZV5iNqTa0fGJpUeN3o 625RUFBQUFD0IooSEw8N7O/2+pun3jFuHbtYunC3dN2Jp9vOPdx9qf7bK/fc rlTuv1zhdvHennNNaw/Vr/qufMm+4hUHBAu3C1w+Lxv7YYiRddQgw9KhpmVG ZtUGRiXfH+rrDlFQUFBQUPQahMLYn346+Oa7e//39XjDYdIx70unrZEu3Cn9 5GfpxlPPvz73ZOfFlp0XHuw4/3Dr6d8/Pfxk+fe/L/ymadHu+9PWVoxaXGo5 scjMLnWwUcKgwfmDjYoGGhbNXSAqY06XpaCgoKCgeDVQJhRmxsTsH2jg9o/X n1vYy0ZOlo6aJ52wQj5lvXzeHtmKH6Rrfmtbe6xt3dEXq354sXR/69xdz1xc Wyavfmw7r278/AqnKYLBphn9B0X2Hxg10IA3wDDD1LxE03AqBQUFBQXFq4Hk O3dW/+3v8f0HyixGyIY7yS0nSJ1mty7e8Mf6b59/uE02eYN07k7p3B3S2Vvb XDY9G/fxHw6LnllMbTj0qzgvX4Q2P/+Cpcvjhwz1feudkLcHRL47MPNK51+j paCgoKCg+Ivi4t493/7zn3JjY7nJMJmVfYvrV1UJqrXG4uKSR27H5E5LZOP+ LRv3UZvTomc2s1tNJ/z+yRcMIfyIiOgFiy++8X/e//d2yOy5NFVLQUFBQfFK okwo3GhvJ+w/UG5k1Pqey72wcHaZlq/c5A7zZCOnSx1mPzWf0GruXB0Vq1Ea 7/z5kwaGZ/u9UalJDgUFBQUFxV8dqXFxh/71L7mBUfOXX4m1fMioPK9AMmWB 4s+aWE94bjb68bxlIqFQm8D8uLgj5maREyfSkJOCgoKC4tXDLxvWNw4YXOt+ mrtY3Q0f+fDRcitniald42+dfDycn57+i62N+PwF/alJQUFBQUHR98jg8c6/ 3b/x+FldCv8x70O52QiZuX1FZFSnhQVZWeGuG8szMnusIwUFBQUFxZ8F57/e 2rD7gI6F689fkps7tNg7l+Tm6lK+ODe3hPImBQUFBcWrgtTkZMGRX3UvLy4t bRsz5cGs+b2nEgUFBQUFxZ8WJfn5XZ2683TpmvQP+uaPV1JQUFBQUPQc/w8M IIOg "], {{0, 0}, {616, 41}}, {0, 255}, ColorFunction -> RGBColor], ImageSize -> {616, 41}, PlotRange -> {{0, 616}, {0, 41}}]], "DockedCell", Background -> GrayLevel[0.866682], CellFrame -> {{0, 0}, {0, 4}}, CellFrameColor -> RGBColor[0.690074, 0.12871, 0.194598], CellMargins -> {{0, 0}, {-3, 0}}, CellFrameMargins -> 0, ContextMenu -> None, ComponentwiseContextMenu -> {}], Cell[ BoxData[ GridBox[{{ GraphicsBox[ RasterBox[CompressedData[" 1:eJztWl1Ik1EYFrqNEoLMbHPmNkRrEhJERj93ra4cJvbDRIsyMk1pc03tTL1w aD+LfkQIJBkR/dBFdtHFDLywCykqoqgLIYRu6jbb8me933e+HT/P2fZN+sZ0 vg9n43zfec973nPe57zvOWNFDS2OhnU5OTlG+LyBj1S/ikAgEAgEAoFAIBAI xEpFMBh8jUgPYG0z7d7MAOYedm/Bko4Ca5tp92YGSCokle5AUiGpdAeSCkml O0RS/R1tjEajUIHvyIhdehPyLNZjrVSAgT5CK1Tmf32e+/qcdYEy+/4+vKTd oQJN89PjojbaHcrCzE8qn0RGfIxrEjcF0SomD49hYqDDUUSGKtUKWRMYz42L pFJDg1RPamGdlRWGuuDi2Yl+WHkoiy72W6jjgFeSm/wWKEAScCvtCxWpSzxt 1FPU9dJ76Lt8UnEmcVMQrWImUQE6nKJB7sgUKpb4LcpEtHiFpEpEKim2TI8n IhXv4pAHXCAJEAPIq7d5JFAOYYEGKHEstTbQAJKSx+XH5ZKKE+CmIFq1ZC/E SBVXoboJyMliKZKKgyapwLlK1ohHKgpYYfGRbnNpg4c8dP3prtckFQ0gUm5K miKpVZxnRZP4KcSziiU1bjhOobpJ2TtIqnhITipYZ7byydJfoDzMpT9ZWMo1 EHbgBBLyhOWzlmakUtKQnB/VuUYkFbWNjZXIJHEKnFVL0t+IXSQVU4iRKkUk JxVzhJI7hirpDpXOGzJ5eFLFvMNORxAlaJZhmtmZStQGAvSQA/FECSksH/kt VLMyokw5qHDOFU3ipiBaxZmtTSo8U2lBI1LF/BWNXZ0Y1LckLo9IqQdYIWdA 9T0uvPT2J2qjrUr2lGMRSzrq4eiIVIxFGC5bMZO4KYhWcWYnSn8gv3j7k+vJ GbVaSNXt9fo6O/XVib9Tpa+sClLdvtB0q+WSvjqRVGucVA/q6p9V1+irE0m1 xkk1cuLk2O49+upEUq1xUg1X14yZraSrS0ed+H+q9GFV/J+qx25/u9U40Nqa aUMQ2YMrFRWf8g0vDh9JvUvgYjPR+8KIyA5AyiNeb1Pe5ql840xxSV97eyq9 Hp1y3nE602waYoXC19GRqInIGHC57lY53Lm53/O2RQ3Fr6qqNXUG609/LLX1 ulOiHyL74D/XeLPxvPiexHDtsuulyexbv2GqwLRgNP8xl/W7XAQE1IUQ1nHw zNl5o2XYoc09RLbC5/E8te26V9+gfskY5SPkuss1abLc2Ljpm9E8Z7FFt++c POroJoQWn1wotQAPj9XMFZp/m6y9bndGpoNYCZBikbNuoqBwsPY4IxIrQJu+ trYf5pLRfOOXotJw6d7Zsv0LtkOPzzb1ENKjolagueVD5YGodUfEZH2372Cm p4X4X/wDFcRtOg== "], {{0, 0}, {199, 30}}, {0, 255}, ColorFunction -> RGBColor], ImageSize -> {199, 30}, PlotRange -> {{0, 199}, {0, 30}}], ButtonBox[ GraphicsBox[ RasterBox[CompressedData[" 1:eJztlDFuhFAMRJHS5w45Re6RI+wFcoOUtNtR0lJSUlNSUtNS0m9JXjTKaPQh UfpgCeT1n2+Px15ebu9vt6eqqp55Xnm+/I/L/p+1bbtt277vvJumIcKbnwWs 73vBsHVdE1bXNQ55Ho8HMOEd3L9tWRZ+6tRBrrjEMAwigHO/37M6SII40zRB Q7QLkpQWjKOu63RqGHHVIoOYYAR16oucinYGxUo2jqMIzPNMnpQRPF2nMkeS cCBDXsm7ZNZp6oZRS3wsIBFNIYM2iY8gYmJA8imqawHcOAKqio4KSp4O7Qjp K1nOUygasaG2hoKSaud3krkArggZzyhhTohP3Uz7E0mNu9g98oj26exOSTon fRUtn8IUJL+W80gyuz6OW3mgrSXXEv5dSaRTaRz9KQpY/knxtVomKdFQxvFT JZFR6pFBJWT5tbEvR9+H3F6S+GOSMC+DTHtrHYyh32Qu855cdhn2CUundjY= "], {{0, 0}, {55, 14}}, {0, 255}, ColorFunction -> RGBColor], ImageSize -> {55, 14}, PlotRange -> {{0, 55}, {0, 14}}], ButtonData -> { URL["http://store.wolfram.com/view/app/playerpro/"], None}, ButtonNote -> "http://store.wolfram.com/view/app/playerpro/"], GraphicsBox[ RasterBox[{{{132, 132, 132}, {156, 155, 155}}, {{138, 137, 137}, { 171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{ 138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, { 171, 169, 169}}, {{135, 135, 135}, {167, 166, 166}}}, {{0, 0}, {2, 14}}, {0, 255}, ColorFunction -> RGBColor], ImageSize -> {2, 14}, PlotRange -> {{0, 2}, {0, 14}}], ButtonBox[ GraphicsBox[ RasterBox[CompressedData[" 1:eJztlSGSg2AMhTuzfu+wB1qzR+gF9gbIWhwSW4lEV1ZWYyvxSPZb3vAmDdDq zpCZdvKH5CUvfwhfx9+f48fhcPjk983vXy922eU9paqqcRx9HGcZhiE+PZ1O KHVd24KOgt0WFKLQ27ZdJrper0JGcS5CVqs6n89yRpGl73tZBK6kkvv97kCe ChOlLEvbVW2kiYPoxKcYRdwWld00jS2EcFSFMYXCqbOcBJzL5aJcxK7SFEFB GQFn8AWupPUkMRfIJEK53W5d1z2hGVP7yohVbfanWoxAJQTfeywbT1+xK9mi GQGTj8FT0uRAN3Tdjl3SlNANP5WoabIIRP+x52ojLEgXs8fxs7+R1cCXNFH6 SVJhKZwx0+BxBZ7nraGNpBSrEFlA1khgRDcCRg1navIWTeVKPVmliaeaL+c4 tCmcknRHfjtWaS6HNtYmC1wYjGJ+6eKjJcficWgVssz1nGbabFtD682gZaIO MHXqkq/vyW3GFaQXliNuOhbz9lOHU3a6SrhWkCmnXC9pUoPBt1aQpquYrtJt 0f6Pazkd497W1MkSlxierkrrN254iz8oHqS0ByzxGzfOHx2yq9plYSl8l13e Xf4ArlmHrg== "], {{0, 0}, {77, 14}}, {0, 255}, ColorFunction -> RGBColor], ImageSize -> {77, 14}, PlotRange -> {{0, 77}, {0, 14}}], ButtonData -> { URL[ "http://www.wolfram.com/solutions/interactivedeployment/\ licensingterms.html"], None}, ButtonNote -> "http://www.wolfram.com/solutions/interactivedeployment/\ licensingterms.html"]}}, ColumnsEqual -> False, GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}]], "DockedCell", Background -> GrayLevel[0.494118], CellFrame -> {{0, 0}, {4, 0}}, CellFrameColor -> RGBColor[0.690074, 0.12871, 0.194598], CellMargins -> 0, CellFrameMargins -> {{0, 0}, {0, -1}}, ContextMenu -> None, ComponentwiseContextMenu -> {}, ButtonBoxOptions -> {ButtonFunction :> (FrontEndExecute[{ NotebookLocate[#2]}]& ), Appearance -> None, ButtonFrame -> None, Evaluator -> None, Method -> "Queued"}]}, FEPrivate`If[ FEPrivate`SameQ[ FrontEnd`CurrentValue[ FrontEnd`EvaluationNotebook[], ScreenStyleEnvironment], "SlideShow"], { Inherited}, {}]], Inherited], FrontEndVersion->"7.0 for Microsoft Windows (32-bit) (November 10, 2008)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[545, 20, 10751, 236, 640, "Output"] } ] *) (* End of internal cache information *) (* NotebookSignature HxTz28v#z7wqAAg#rj1FSQz8 *)