T745 - Content-type application/mathematica...

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(************** 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: [email protected] phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 54363, 1405]*) (*NotebookOutlinePosition[ 54995, 1427]*) (* CellTagsIndexPosition[ 54951, 1423]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ Cell[BoxData[{ \(TraditionalForm\`u''\ + \ u\ + \ x\ = \ 0, \ 0 < x < 1\ \), "\[IndentingNewLine]", \(TraditionalForm\`u( 0)\ = \ \(\(u(1)\)\(\ \)\(=\)\(\ \)\(0\)\(\ \)\)\)}]], "\n\na) Weak form: multiply differential equation by admissible virtual \ field \[Delta]u, integrate between (0,1), integrate by parts:\n", Cell[BoxData[ \(TraditionalForm\`0 = \(\[Integral]\_0\%1\((u''\ + \ u\ + \ x)\)\ \[Delta]u \[DifferentialD]x\ = \[IndentingNewLine]\(\
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\[Integral]\_0\%1\((\(-u'\)\ \[Delta]u'\ + \ \((u'\ \[Delta]u)\)'\ + \ u\ \[Delta]u\ + \ x\ \[Delta]u)\)\ \[DifferentialD]x\ = \ \[IndentingNewLine]\ \ u'\ \[Delta]u\( | \ \_0\)\^1\(+\(\[Integral]\_0\%1\((\(-u'\)\ \[Delta]u'\ \ + \ u\ \[Delta]u\ + \ x\ \[Delta]u)\)\ \[DifferentialD]x\)\)\)\)\)]], "\n\nAdmissibility requires the boundary terms to vanish, The weak form is \ therefore:\n", Cell[BoxData[ \(TraditionalForm\`\[Integral]\_0\%1\((\(-u'\)\ \[Delta]u'\ \ + \ u\ \[Delta]u\ + \ x\ \[Delta]u)\)\ \[DifferentialD]x = 0, \ \[ForAll] \ \[Delta]u\ s . t . \ \(\[Delta]u(0)\)\ = \ \(\[Delta]u(1)\ = \ 0\)\)]], "\n" }], "Subtitle"], Cell["Approximation:", "Subtitle"], Cell[BoxData[{ \(\[CapitalPhi][n_] := Table[\[Phi]\_i = \ x\ \((1 - x)\)\ x\^\(i - 1\), {i, n}]\), "\[IndentingNewLine]", \(Ck[n_]\ := \ Table\ [c[i], {i, n}]\), "\[IndentingNewLine]", \(U\_N[n_]\
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This note was uploaded on 11/07/2011 for the course AERO 16.21 taught by Professor Dffs during the Fall '10 term at MIT.

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T745 - Content-type application/mathematica...

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