(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 8.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 13238, 300] NotebookOptionsPosition[ 12008, 271] NotebookOutlinePosition[ 12356, 286] CellTagsIndexPosition[ 12313, 283] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[TextData[StyleBox["\:0423\:043f\:0440\:0430\:0436\:043d\:0435\:043d\:0438\ \:044f 5-6.\n\:041d\:044f\:043a\:043e\:0438 \:043f\:0440\:0430\:043a\:0442\ \:0438\:0447\:0435\:0441\:043a\:0438 \:0432\:044a\:043f\:0440\:043e\:0441\ \:0438, \:0441\:0432\:044a\:0440\:0437\:0430\:043d\:0438 \:0441 \:0438\:043d\ \:0442\:0435\:0440\:043f\:043e\:043b\:0430\:0446\:0438\:044f\:0442\:0430, \ \:0438 \:043f\:0440\:0438\:043b\:043e\:0436\:0435\:043d\:0438\:044f", FontFamily->"Arial Narrow"]], "Title", CellChangeTimes->{{3.5598332706406136`*^9, 3.5598332787214403`*^9}, { 3.623675754512615*^9, 3.623675786262059*^9}, {3.6243603756086206`*^9, 3.6243603778451996`*^9}},ExpressionUUID->"81768e03-6543-4c95-ab08-\ 2f6d2d2da33c"], Cell[CellGroupData[{ Cell[TextData[StyleBox["\:0417\:0430\:0434\:0430\:0447\:0430 1: \:0414\:0430 \ \:0441\:0435 \:043d\:0430\:043f\:0438\:0448\:0435 \:0444\:0443\:043d\:043a\ \:0446\:0438\:044f newtonPoly[nodes_,values_,x_], \:043a\:043e\:044f\:0442\ \:043e \:0432\:0440\:044a\:0449\:0430 \:0432 \:043d\:043e\:0440\:043c\:0430\ \:043b\:0435\:043d \:0432\:0438\:0434 \:043f\:043e\:043b\:0438\:043d\:043e\ \:043c\:0430 \:043d\:0430 \:041d\:044e\:0442\:043e\:043d p(x) \:0437\:0430 \ \:0432\:044a\:0437\:043b\:0438\:0442\:0435 nodes \:0438 \:0441\:0442\:043e\ \:0439\:043d\:043e\:0441\:0442\:0438 values.", FontFamily->"Times New Roman"]], "Subsubsection", CellChangeTimes->{{3.623676519466811*^9, 3.623676584127553*^9}, { 3.718941330405058*^9, 3.7189413339050627`*^9}},ExpressionUUID->"8e0d4eb0-e617-40e2-8753-\ 554816c8f0d9"], Cell[BoxData[ RowBox[{ RowBox[{"dividedDiff", "[", RowBox[{"nodes_", ",", "values_"}], "]"}], ":=", RowBox[{"(", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Length", "[", "nodes", "]"}], "\[Equal]", "1"}], ",", "\[IndentingNewLine]", RowBox[{"values", "[", RowBox[{"[", "1", "]"}], "]"}], ",", "\[IndentingNewLine]", FractionBox[ RowBox[{"(", RowBox[{ RowBox[{"dividedDiff", "[", RowBox[{ RowBox[{"nodes", "[", RowBox[{"[", RowBox[{"2", ";;", RowBox[{"Length", "[", "nodes", "]"}]}], "]"}], "]"}], ",", RowBox[{"values", "[", RowBox[{"[", RowBox[{"2", ";;", RowBox[{"Length", "[", "nodes", "]"}]}], "]"}], "]"}]}], "]"}], "-", RowBox[{"dividedDiff", "[", RowBox[{ RowBox[{"nodes", "[", RowBox[{"[", RowBox[{"1", ";;", RowBox[{ RowBox[{"Length", "[", "nodes", "]"}], "-", "1"}]}], "]"}], "]"}], ",", RowBox[{"values", "[", RowBox[{"[", RowBox[{"1", ";;", RowBox[{ RowBox[{"Length", "[", "nodes", "]"}], "-", "1"}]}], "]"}], "]"}]}], "]"}]}], ")"}], RowBox[{ RowBox[{"nodes", "[", RowBox[{"[", RowBox[{"Length", "[", "nodes", "]"}], "]"}], "]"}], "-", RowBox[{"nodes", "[", RowBox[{"[", "1", "]"}], "]"}]}]]}], "]"}], "\[IndentingNewLine]", ")"}]}]], "Input", CellChangeTimes->{{3.557338163499015*^9, 3.5573383204106464`*^9}, { 3.5573383554459934`*^9, 3.557338455564543*^9}, {3.5573386632217035`*^9, 3.5573386659592304`*^9}, 3.5607456818594723`*^9, {3.560745884868164*^9, 3.5607458883133717`*^9}, {3.62367607819716*^9, 3.6236762290367393`*^9}, { 3.6236762766597834`*^9, 3.6236763123659983`*^9}, {3.6243488308422575`*^9, 3.6243488492279882`*^9}, {3.624350059325478*^9, 3.6243500826987605`*^9}, { 3.6243510148566856`*^9, 3.6243510674015665`*^9}, {3.6243511223133287`*^9, 3.624351132510521*^9}, {3.624351250404334*^9, 3.624351290846847*^9}, { 3.6570469747217846`*^9, 3.657047035008679*^9}, {3.7825342073498464`*^9, 3.7825342111336627`*^9}},ExpressionUUID->"8f1b47e2-fee0-4b86-82f3-\ d23d6bb76117"] }, Open ]], Cell[TextData[{ StyleBox["\:0417\:0430\:0434\:0430\:0447\:0430", FontFamily->"Times New Roman"], " ", StyleBox["2: \:0412 \:0442\:0430\:0431\:043b\:0438\:0446\:0430\:0442\:0430 \ \:0441\:0430 \:0434\:0430\:0434\:0435\:043d\:0438 \:0434\:0430\:043d\:043d\ \:0438 \:0437\:0430 \:043d\:0430\:0441\:0435\:043b\:0435\:043d\:0438\:0435\ \:0442\:043e \:043d\:0430 \:0421\:0410\:0429 \:0432 \:043f\:0435\:0440\:0438\ \:043e\:0434\:0430 1920-1990. \:0414\:0430 \:0441\:0435 \:043f\:043e\:0441\ \:0442\:0440\:043e\:0438 \:043f\:043e\:043b\:0438\:043d\:043e\:043c \:043e\ \:0442 \:0441\:0435\:0434\:043c\:0430 \:0441\:0442\:0435\:043f\:0435\:043d, \ \:0438\:043d\:0442\:0435\:0440\:043f\:043e\:043b\:0438\:0440\:0430\:0449 \ \:0442\:0430\:0431\:043b\:0438\:0446\:0430\:0442\:0430.\n \:0414\:0430 \:0441\ \:0435 \:0434\:0430\:0434\:0435 \:043f\:0440\:0438\:0431\:043b\:0438\:0436\ \:0435\:043d\:0438\:0435 \:043d\:0430 \:043d\:0430\:0441\:0435\:043b\:0435\ \:043d\:0438\:0435\:0442\:043e \:043f\:0440\:0435\:0437 1952, 1974, 2000 \ \:0433\:043e\:0434\:0438\:043d\:0430 \:0438 \:0434\:0430 \:0441\:0435 \:0441\ \:0440\:0430\:0432\:043d\:0438 \:0441 \:0434\:0435\:0439\:0441\:0442\:0432\ \:0438\:0442\:0435\:043b\:043d\:0438\:0442\:0435 \:0441\:0442\:043e\:0439\ \:043d\:043e\:0441\:0442\:0438 - \:0441\:044a\:043e\:0442\:0432\:0435\:0442\ \:043d\:043e\n 157\:043c\:043b\:043d, 214 \:043c\:043b\:043d, 281.42\:043c\ \:043b\:043d.", FontFamily->"Arial Narrow"], "\n ", Cell[BoxData[GridBox[{ {"\:0433\:043e\:0434\:0438\:043d\:0430", "1920", "1930", "1940", "1950", "1960", "1970", "1980", "1990"}, {"\:043d\:0430\:0441\:0435\:043b\:0435\:043d\:0438\:0435", "106.46", "123.08", "132.12", "152.27", "180.67", "205.05", "227.23", "249.46"} }, GridBoxDividers->{ "Columns" -> {{True}}, "ColumnsIndexed" -> {}, "Rows" -> {{True}}, "RowsIndexed" -> {}}]],ExpressionUUID-> "a7544676-c384-460e-8e19-6163ed7f1db0"] }], "Subsubsection", CellChangeTimes->{{3.591959992925702*^9, 3.5919601837576776`*^9}, { 3.5919602230523496`*^9, 3.5919602260955563`*^9}, 3.623675828862109*^9, 3.6236758827011385`*^9, {3.6871767278413115`*^9, 3.687176729614314*^9}, { 3.6871767697963734`*^9, 3.6871767807163887`*^9}},ExpressionUUID->"16b3a077-c76b-42eb-a961-\ 24b445e7bc6f"], Cell[TextData[{ StyleBox["\:0417\:0430\:0434\:0430\:0447\:0430 3: \:0414\:0430 \:0441\:0435 \ \:043f\:0440\:0438\:0431\:043b\:0438\:0436\:0438 \:0444\:0443\:043d\:043a\ \:0446\:0438\:044f\:0442\:0430 ", FontFamily->"Arial Narrow"], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ RowBox[{"f", "(", "x", ")"}], "=", FractionBox["1", RowBox[{"1", "+", RowBox[{"25", SuperscriptBox["x", "2"]}]}]]}], ",", " "}], TraditionalForm]], FontFamily->"Arial Narrow",ExpressionUUID-> "edc0e159-eb02-4319-b38d-1b6162ed6538"], StyleBox["\:043a\:0430\:0442\:043e \:0441\:0435 \:0438\:0437\:043f\:043e\ \:043b\:0437\:0432\:0430\:0442 \:043f\:043e\:043b\:0438\:043d\:043e\:043c\ \:0438 \:043e\:0442 \:0441\:0442\:0435\:043f\:0435\:043d\:0438 10 \:0438 4.", FontFamily->"Arial Narrow"], "\n", StyleBox[" \:0414\:0430 \:0441\:0435 \:043f\:043e\:0441\:0442\:0440\:043e\ \:044f\:0442 \:0433\:0440\:0430\:0444\:0438\:043a\:0438\:0442\:0435 \:043d\ \:0430 \:0433\:0440\:0435\:0448\:043a\:0438\:0442\:0435 (\:043f\:043e \:0430\ \:0431\:0441. \:0441\:0442\:043e\:0439\:043d\:043e\:0441\:0442) \:0432 \ \:0434\:0432\:0430\:0442\:0430 \:0441\:043b\:0443\:0447\:0430\:044f", FontFamily->"Arial Narrow"] }], "Subsubsection", CellChangeTimes->{{3.5919606055203557`*^9, 3.5919606572668743`*^9}, { 3.6236758708187313`*^9, 3.6236759374327664`*^9}},ExpressionUUID->"2bdf9e15-69b9-4fe2-b79f-\ 53f77e5bdc7e"], Cell[CellGroupData[{ Cell["\:0417\:0430\:0434\:0430\:0447\:0430 4: \:0414\:0430 \:0441\:0435 \ \:0441\:044a\:0441\:0442\:0430\:0432\:0438 \:0430\:043d\:0438\:043c\:0430\ \:0446\:0438\:044f \:043f\:043e \:0437\:0430\:0434\:0430\:0434\:0435\:043d\ \:0438\:0442\:0435 \:0441\:0446\:0435\:043d\:0438:", "Subsubsection", CellChangeTimes->{{3.5919606055203557`*^9, 3.5919606572668743`*^9}, { 3.6236758708187313`*^9, 3.6236759374327664`*^9}, {3.623686900322296*^9, 3.623686904069913*^9}, {3.6236872309132423`*^9, 3.623687241907033*^9}}, FontFamily-> "Arial Narrow",ExpressionUUID->"055d01c7-e578-459d-b7f4-61cb594a3cca"], Cell[BoxData[ RowBox[{ GraphicsBox[CircleBox[{0, 0}, 0.1], Axes->True, AxesOrigin->{0, 0}, ImageSize->{183.33333333333334`, Automatic}, PlotRange->{{-0.5, 1}, {-0.5, 1}}], GraphicsBox[CircleBox[{0.2, 0.5}, 0.1], Axes->True, AxesOrigin->{0, 0}, ImageSize->{185.33333333333334`, Automatic}, PlotRange->{{-0.5, 1}, {-0.5, 1}}], GraphicsBox[CircleBox[{0.4, 0.8}, 0.1], Axes->True, AxesOrigin->{0, 0}, ImageSize->{187.99999999999994`, Automatic}, PlotRange->{{-0.5, 1}, {-0.5, 1}}]}]], "Input", CellChangeTimes->{{3.6211620760909023`*^9, 3.6211620851378636`*^9}}, FontFamily-> "Arial Narrow",ExpressionUUID->"25cc64be-6c2c-448c-a91e-98b5611c570f"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "\:0417\:0430\:0434\:0430\:0447\:0430 5 : \:041f\:0440\:043e\:0432\:0435\ \:0434\:0435\:043d\:0438 \:0441\:0430 \:0435\:043a\:0441\:043f\:0435\:0440\ \:0438\:043c\:0435\:043d\:0442\:0438, \:0437\:0430 \:0434\:0430 \:0441\:0435 \ \:043e\:043f\:0440\:0435\:0434\:0435\:043b\:0438 \:0431\:044a\:0440\:0437\ \:043e\:0434\:0435\:0439\:0441\:0442\:0432\:0438\:0435\:0442\:043e \:043d\ \:0430 \:0435\:0434\:0438\:043d \:0430\:043b\:0433\:043e\:0440\:0438\:0442\ \:044a\:043c \:0437\:0430 \:0441\:043e\:0440\:0442\:0438\:0440\:0430\:043d\ \:0435 \:0432 \:0437\:0430\:0432\:0438\:0441\:0438\:043c\:043e\:0441\:0442 \ \:043e\:0442 \:0431\:0440\:043e\:044f \:0435\:043b\:0435\:043c\:0435\:043d\ \:0442\:0438. \:0420\:0435\:0437\:0443\:043b\:0442\:0430\:0442\:0438\:0442\ \:0435 \:0441\:0430 \:043f\:0440\:0435\:0434\:0441\:0442\:0430\:0432\:0435\ \:043d\:0438 \:0432 \:0441\:043b\:0435\:0434\:043d\:0430\:0442\:0430 \:0442\ \:0430\:0431\:043b\:0438\:0446\:0430:\n", Cell[BoxData[GridBox[{ { RowBox[{ RowBox[{ RowBox[{"\:0431\:0440", ".", " ", "\:0435"}], "/", "\:0442\:0438"}], ",", " ", "\:0445\:0438\:043b"}], "10", "20", "50", "100", "150", "200", "250"}, { RowBox[{"\:0432\:0440\:0435\:043c\:0435", ",", " ", "s"}], "0.1639275", "0.53282", "3.00007", "11.20784", "26.7486723", "47.3297", "76.80605"} }, GridBoxDividers->{ "Columns" -> {{True}}, "ColumnsIndexed" -> {}, "Rows" -> {{True}}, "RowsIndexed" -> {}}]],ExpressionUUID-> "8d24f065-b023-4c94-879f-cf0a62a12f2a"], "\n", "\:0414\:0430 \:0441\:0435 \:043e\:043f\:0440\:0435\:0434\:0435\:043b\:0438 \ \:043a\:043e\:043b\:043a\:043e \:043d\:0430\:0439-\:043c\:043d\:043e\:0433\ \:043e \:0435\:043b\:0435\:043c\:0435\:043d\:0442\:0430 \:043c\:043e\:0433\ \:0430\:0442 \:0434\:0430 \:0441\:0435 \:0441\:043e\:0440\:0442\:0438\:0440\ \:0430\:0442 \:0437\:0430 \:043d\:0435 \:043f\:043e\:0432\:0435\:0447\:0435 \ \:043e\:0442 30\:0441\:0435\:043a.", "\n" }], "Subsubsection", CellChangeTimes->{{3.624354407739175*^9, 3.6243545938496084`*^9}}, FontFamily-> "Arial Narrow",ExpressionUUID->"3c74240f-1862-4d99-8cc9-1792678cd5a5"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.7189411563902545`*^9, 3.718941207202512*^9}},ExpressionUUID->"90348c84-b486-48ce-b134-\ 336594ce7360"] }, Open ]] }, Open ]] }, WindowSize->{1920, 998}, WindowMargins->{{-8, Automatic}, {Automatic, -8}}, FrontEndVersion->"11.2 for Microsoft Windows (64-bit) (September 10, 2017)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[579, 22, 723, 10, 150, "Title",ExpressionUUID->"81768e03-6543-4c95-ab08-2f6d2d2da33c"], Cell[CellGroupData[{ Cell[1327, 36, 811, 12, 63, "Subsubsection",ExpressionUUID->"8e0d4eb0-e617-40e2-8753-554816c8f0d9"], Cell[2141, 50, 2369, 57, 195, "Input",ExpressionUUID->"8f1b47e2-fee0-4b86-82f3-d23d6bb76117"] }, Open ]], Cell[4525, 110, 2293, 40, 149, "Subsubsection",ExpressionUUID->"16b3a077-c76b-42eb-a961-24b445e7bc6f"], Cell[6821, 152, 1431, 31, 68, "Subsubsection",ExpressionUUID->"2bdf9e15-69b9-4fe2-b79f-53f77e5bdc7e"], Cell[CellGroupData[{ Cell[8277, 187, 601, 8, 35, "Subsubsection",ExpressionUUID->"055d01c7-e578-459d-b7f4-61cb594a3cca"], Cell[8881, 197, 691, 19, 202, "Input",ExpressionUUID->"25cc64be-6c2c-448c-a91e-98b5611c570f"] }, Open ]], Cell[CellGroupData[{ Cell[9609, 221, 2160, 40, 171, "Subsubsection",ExpressionUUID->"3c74240f-1862-4d99-8cc9-1792678cd5a5"], Cell[11772, 263, 208, 4, 67, "Input",ExpressionUUID->"90348c84-b486-48ce-b134-336594ce7360"] }, Open ]] }, Open ]] } ] *)