This is pdfTeX, Version 3.1415926-1.40.10 (MiKTeX 2.8) (preloaded format=pdflatex 2010.2.1)  11 FEB 2010 22:21
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**A:/My*CSM/06*Sping*2010/01*EOR/02*HW/HW2/RHS.tex
("A:/My CSM/06 Sping 2010/01 EOR/02 HW/HW2/RHS.tex"
LaTeX2e <2009/09/24>
Babel <v3.8l> and hyphenation patterns for english, dumylang, nohyphenation, german, ngerman, german-x-2009-06-19, ngerm
an-x-2009-06-19, french, loaded.

! LaTeX Error: Missing \begin{document}.

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l.1 R
     ecall RHS of Eq(\ref{mass})
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<write> ...ing: Reference `mass' on page \thepage 
                                                  \space undefined\on@line .
l.1 Recall RHS of Eq(\ref{mass}
                               )
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


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! LaTeX Error: Missing \begin{document}.

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l.3 \begin{equation}
                    \label{mass_R}
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l.7 L
     et's define $A_c=\phi\left(X_c\xi_oS_o+Y_c\xi_gS_g+W_c\xi_wS_w\right)$ ...
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! Undefined control sequence.
<write> ...g: Reference `mass_R' on page \thepage 
                                                  \space undefined\on@line .
l.7 ...wS_w\right)$ and discretize Eq(\ref{mass_R}
                                                  ) in time space we get
The control sequence at the end of the top line
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l.9 \begin{equation}
                    \label{RHS}
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l.13 U
      sing Taylor's series to expand $A_c^{n+1}$ as follows
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l.15 \begin{equation}
                     \label{R_taylor}
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[]\OML/cmm/m/it/10 A[] \OT1/cmr/m/n/10 = \OML/cmm/m/it/10 A[] \OT1/cmr/m/n/10 + [][] \OML/cmm/m/it/10 P[] \OT1/cmr/m/n/
10 + [][] \OML/cmm/m/it/10 S[] \OT1/cmr/m/n/10 + [][] \OML/cmm/m/it/10 S[] \OT1/cmr/m/n/10 + [] []
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! LaTeX Error: Missing \begin{document}.

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l.19 L
      et's expand Eq(\ref{R_taylor}) term by term
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! Undefined control sequence.
<write> ... Reference `R_taylor' on page \thepage 
                                                  \space undefined\on@line .
l.19 Let's expand Eq(\ref{R_taylor}
                                   ) term by term
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


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l.21 \begin{equation}
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l.28 \begin{equation}
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l.35 \begin{equation}
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l.42 F
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l.44 \begin{equation}
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l.52 \begin{equation}
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l.60 F
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l.62 \begin{equation}
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l.70 \begin{equation}
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l.78 F
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l.80 \begin{equation}
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l.89 \begin{equation}
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! LaTeX Error: Missing \begin{document}.

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l.98 S
      ubstitute Eq (\ref{R_taylor}) - (\ref{R_y3}) into Eq (\ref{RHS})
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<write> ... Reference `R_taylor' on page \thepage 
                                                  \space undefined\on@line .
l.98 Substitute Eq (\ref{R_taylor}
                                  ) - (\ref{R_y3}) into Eq (\ref{RHS})
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


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<write> ...ing: Reference `R_y3' on page \thepage 
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l.98 Substitute Eq (\ref{R_taylor}) - (\ref{R_y3}
                                                 ) into Eq (\ref{RHS})
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misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Reference `R_y3' on page  undefined on input line 98.

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<write> ...ning: Reference `RHS' on page \thepage 
                                                  \space undefined\on@line .
l.98 ...taylor}) - (\ref{R_y3}) into Eq (\ref{RHS}
                                                  )
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


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l.100 f
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