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{\newpage
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\samepage \begin{displaymath}(y-f(x^0)) = f'(x^0) \,(x-x^0) ~~~~~.
\end{displaymath}
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{\newpage
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\samepage \begin{eqnarray*}0-f(x^0)) &=& f'(x^0) \,(x-x^0)  \\ 
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\end{eqnarray*}
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{\newpage
\clearpage
\samepage \begin{eqnarray*}0-f(x^j)) &=& \frac{f(x^j) - f(x^{j-1})}{x^j-x^{j-1}} \,(x-x^{j})  \\ 
x^j - \frac{f(x^j) (x^j-x^{j-1})}{f(x^j) - f(x^{j-1})} &=& x  ~~~~.
\end{eqnarray*}
}

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{\newpage
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\end{displaymath}
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{\newpage
\clearpage
\samepage \begin{displaymath}f(x+\Delta x) \approx f(x) + f'(x) (x+\Delta x - x) + \frac{1}{2}
f''(x) (x+\Delta x - x)^2 + \dots
\end{displaymath}
}

{\newpage
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{\newpage
\clearpage
\samepage \begin{displaymath}f'(x) = \frac{f(x+\Delta x) -f(x)}{x+\Delta x - x} ~-{error}
\end{displaymath}
}

{\newpage
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{\newpage
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{\newpage
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{\newpage
\clearpage
\samepage \begin{displaymath}f'(x) = \displaystyle{\lim_{\Delta x \rightarrow 0}}
\frac{f(x+\Delta x)-f(x-\Delta x)}{2 \Delta x} ~.
\end{displaymath}
}

{\newpage
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\stepcounter{section}
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{\newpage
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{\newpage
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\stepcounter{subsection}
\stepcounter{subsection}
{\newpage
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\samepage \setbox\sizebox=\hbox{$f(x)=f(a) + f'(a)(x-a) + f'' (\xi) \frac{(x-a)^2}{2}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline499: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
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}

{\newpage
\clearpage
\samepage \begin{eqnarray*}\int_a^b f(x) dx &=& \int_a^b (f(a) + f'(a)(x-a) +
     f'' (\xi) \frac{(x-a)^2}{2}  \\ 
~&=& (b-a)f(a) + f'(a)(\frac{x^2}{2} - ax)_a^b +
     f''(\xi) (\frac{(x-a)^3}{6})_a^b \\ 
~&=& (b-a) \frac{f(a)+f(b)}{2} + C (b-a)^3
\end{eqnarray*}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$E \approx C (\Delta x)^3$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline511: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
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\samepage \setbox\sizebox=\hbox{$C N (\Delta x)^3 = C (\Delta x)^2$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline513: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
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\samepage \setbox\sizebox=\hbox{$f(x)=f(a) + f'(\xi)(x-a)$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline515: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
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{\newpage
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\stepcounter{section}
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\samepage \setbox\sizebox=\hbox{$\frac{dy}{dt} = y$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline521: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
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\samepage \setbox\sizebox=\hbox{$y= a \exp(t)$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline523: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
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{\newpage
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\samepage \setbox\sizebox=\hbox{$y(t=0) = 2$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline527: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
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{\newpage
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\samepage \setbox\sizebox=\hbox{$\Delta t$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline531: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$t^n = n \Delta t ,~ y^n = y(t^n)$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline533: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$y^{n-1}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline535: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
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\samepage \setbox\sizebox=\hbox{$t^{n} $}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline537: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \begin{displaymath}\frac{y^{n}-y^{n-1}}{\Delta t} = y^{n-1}
\end{displaymath}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$y^{n}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline541: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \begin{displaymath}y^{n}~=~y^{n-1} + \Delta t y^{n-1}
\end{displaymath}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$\Delta t$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline545: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
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\samepage \setbox\sizebox=\hbox{$t^0 = 0$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline547: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
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\samepage \setbox\sizebox=\hbox{$t^1 = \Delta t$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline549: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
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\samepage \setbox\sizebox=\hbox{$n=0,~y^0=2.0$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline551: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
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\samepage \setbox\sizebox=\hbox{$y^*$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline553: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \begin{eqnarray*}\frac{dW}{dt} &=& (a1+b1D)W  \\ 
\frac{dD}{dt} &=& (c1-d1W)D  ~~~.
\end{eqnarray*}
}

\stepcounter{section}
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{\newpage
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{\newpage
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\samepage \setbox\sizebox=\hbox{$f(x)=8x^3 + 2x^2 -5x +1$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline561: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
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{\newpage
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{\newpage
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{\newpage
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{\newpage
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\samepage \setbox\sizebox=\hbox{$G(x) = \int_0^x e^{-y^2 /2} \,dy$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline575: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
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\samepage \setbox\sizebox=\hbox{$\frac{dy}{dt} = \frac{-t}{y},~ y(0)=1$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline581: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

\stepcounter{section}

\end{document}
