(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 13.3' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 186201, 3250] NotebookOptionsPosition[ 184383, 3212] NotebookOutlinePosition[ 184830, 3229] CellTagsIndexPosition[ 184787, 3226] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Serie di Fourier dell\[CloseCurlyQuote]onda quadra", "Title", CellChangeTimes->{{3.9088594508779526`*^9, 3.9088594706393323`*^9}, { 3.9088595084627647`*^9, 3.9088596249600964`*^9}, {3.9088597245145273`*^9, 3.908859744304455*^9}, {3.9088598452016416`*^9, 3.9088599204696903`*^9}, { 3.908860687473818*^9, 3.9088607127373176`*^9}},ExpressionUUID->"94901225-1ca2-4773-bf37-\ 12b4b6593907"], Cell[TextData[{ "In questo Notebook calcoliamo delle somme parziali della serie di Fourier \ dell\[CloseCurlyQuote]onda quadra. Ci\[OGrave] ci permette di avere una \ visualizzazione empirica della convergenza della serie\nCominciamo con lo \ scrivere la somma parziale della sdF in forma trigonometrica nel caso T=1: \n", Cell[BoxData[ FormBox[ TemplateBox[<|"boxes" -> FormBox[ RowBox[{ StyleBox["x", "TI"], RowBox[{"(", StyleBox["t", "TI"], ")"}], "\[LongEqual]", FractionBox["1", "2"], "+", UnderoverscriptBox["\[Sum]", RowBox[{ StyleBox["m", "TI"], "\[LongEqual]", "0"}], RowBox[{"+", "\[Infinity]"}], LimitsPositioning -> True], FractionBox[ SuperscriptBox[ RowBox[{"(", "-1", ")"}], StyleBox["m", "TI"]], RowBox[{ RowBox[{"(", RowBox[{"2", StyleBox["m", "TI"], "+", "1"}], ")"}], "\[Pi]"}]], "cos", RowBox[{"[", RowBox[{ RowBox[{"(", RowBox[{"2", StyleBox["m", "TI"], "+", "1"}], ")"}], "2", "\[Pi]", StyleBox["t", "TI"]}], "]"}]}], TraditionalForm], "errors" -> {}, "input" -> "$x(t)=\\frac{1}{2}+\\sum_{m =0}^{+\\infty} \ \\frac{(-1)^m}{(2m+1)\\pi}\\cos[(2m+1)2\\pi t]$", "state" -> "Boxes"|>, "TeXAssistantTemplate"], 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