T747 - (************** Content-type:...

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Unformatted text preview: (************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' 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). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. 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[ 273578, 4625]*) (*NotebookOutlinePosition[ 274264, 4649]*) (* CellTagsIndexPosition[ 274220, 4645]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[StyleBox["Question 1: Problem 7.47 from textbook", "Section \ 1"]], "Subtitle"], Cell[BoxData[ \(\(\( (*\ clean\ all\ the\ variables\ \ *) \)\(\[IndentingNewLine]\)\(Clear["\<Global`*\>"]; Off[General::spell, General::spell1];\)\)\)], "Input", FontSize->24], Cell[CellGroupData[{ Cell["1) approximation functions (two families):", "Subtitle", FontSize->24], Cell[BoxData[ \(\(\(\[Phi]k[n_]\ := \ Table[\[Phi]\_i = Cos[\((2\ i - 1)\) \(\[Pi]\/2\) x\_1]\ Cos[\((2\ i - 1)\) \(\[Pi]\/2\) x\_2], {i, n}]\)\(\[IndentingNewLine]\)\( (*\[Phi]k[n_]\ := \ Table[\[Phi]\_i = \((x\_1\^i - 1)\) \((x\_2\^i - 1)\), {i, n}]*) \)\(\[IndentingNewLine]\) \)\)], "Input", FontSize->24] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ \(\[Phi]k[2]\), "\[IndentingNewLine]", \(\[Phi]\_2\)}], "Input"], Cell[BoxData[ \({Cos[\(\[Pi]\ x\_1\)\/2]\ Cos[\(\[Pi]\ x\_2\)\/2], Cos[\(3\ \[Pi]\ x\_1\)\/2]\ Cos[\(3\ \[Pi]\ x\_2\)\/2]}\)], "Output"], Cell[BoxData[ \(Cos[\(3\ \[Pi]\ x\_1\)\/2]\ Cos[\(3\ \[Pi]\ x\_2\)\/2]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\((\[PartialD]\_\(x\_1\)\[Phi]\_1)\)\^2 // Simplify\)], "Input"], Cell[BoxData[ \(1\/4\ \[Pi]\^2\ Cos[\(\[Pi]\ x\_2\)\/2]\^2\ Sin[\(\[Pi]\ \ x\_1\)\/2]\^2\)], "Output"] }, Open ]], Cell[BoxData[ \(Stiffness[n_]\ := \ Table[\ \[Integral]\_0\%1\(\[Integral]\_0\%1\((\((\[PartialD]\_\(x\_1\)\...
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T747 - (************** Content-type:...

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