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Cell[CellGroupData[{
Cell["Chapter 6, Section 6, Problem 6 (page 118-119)", "Subtitle"],

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    \(\(b = 0.09;\)\), "\[IndentingNewLine]", 
    \(\(y0 = 0;\)\)}], "Input"],

Cell[BoxData[
    \(\(\( (*\ 
      create\ the\ functional\ mappings\ *) \)\(\[IndentingNewLine]\)\(\(sMap[
          y_] := a\ x\ y\^2 + b\ E\^\(-x\) - 
          a\ \(E\^\(-x\)\) 
            Integrate[\(E\^s\) \((y /. {x \[Rule] s})\)\^2, {s, 1, 
                x}];\)\[IndentingNewLine]
    \(tMap[t_] := b + 2\ a\ t\^2;\)\)\)\)], "Input"],

Cell[BoxData[{
    \(nIters = 5; \ \  (*\ 
      the\ number\ of\ Newton\ iterations\ to\ perform\ \
*) \[IndentingNewLine]theSIters = 
      FixedPointList[sMap, y0, nIters];\), "\[IndentingNewLine]", 
    \(\(theTIters = FixedPointList[tMap, 0, nIters];\)\)}], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(\(\( (*\ 
      plot\ the\ functional\ iterations\ *) \)\(\[IndentingNewLine]\)\(Plot[
        Evaluate[theSIters], {x, 0, 1}];\)\)\)], "Input"],

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