\relax 
\@writefile{toc}{\contentsline {chapter}{Preface}{i}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {chapter}{\numberline {1}Introduction}{1}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {chapter}{\numberline {2}Sources of Error}{3}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{se*se}{{2}{3}}
\@writefile{toc}{\contentsline {section}{\numberline {2.1}Relative and absolute error}{3}}
\newlabel{RelAbsErr*se}{{2.1}{3}}
\newlabel{error*se}{{2.1}{4}}
\@writefile{toc}{\contentsline {section}{\numberline {2.2}Computer arithmetic}{4}}
\newlabel{CompArith*se}{{2.2}{4}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2.1}Introducing the standard}{5}}
\newlabel{IEEE*se}{{2.2.1}{5}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2.2}Representation of numbers, arithmetic operations}{5}}
\newlabel{ieee*se}{{2.2}{6}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2.3}Exceptions}{7}}
\@writefile{lof}{\contentsline {figure}{\numberline {2.1}{\ignorespaces \it  A program that illustrates some of the features of arithmetic using the IEEE floating point standard.}}{10}}
\newlabel{SourcesOfError.C*se}{{2.1}{10}}
\@writefile{toc}{\contentsline {section}{\numberline {2.3}Truncation error}{10}}
\newlabel{TruncErr*se}{{2.3}{10}}
\newlabel{fp*se}{{2.3}{10}}
\newlabel{TrunkTable*se}{{2.3}{11}}
\@writefile{lof}{\contentsline {figure}{\numberline {2.2}{\ignorespaces Estimates of $f^{\prime }(x)$ using (2.3\hbox {}). The error is $e_{tot}$, which is a combination of truncation and roundoff error. Roundoff error is apparent only in the last two estimates.}}{11}}
\newlabel{ItTable*se}{{2.4}{11}}
\@writefile{lof}{\contentsline {figure}{\numberline {2.3}{\ignorespaces Iterates of $x_{n+1} = \mathop {\mathgroup \symoperators ln}\nolimits (y) - \mathop {\mathgroup \symoperators ln}\nolimits (x_n)$ illustrating convergence to a limit that satisfies the equation $xe^x = y$. The error is $e_n = x_n - x$. Here, $y=10$.}}{11}}
\@writefile{toc}{\contentsline {section}{\numberline {2.4}Iterative Methods}{11}}
\newlabel{IterErr*se}{{2.4}{11}}
\@writefile{toc}{\contentsline {section}{\numberline {2.5}Statistical error in Monte Carlo}{11}}
\newlabel{StatErr*se}{{2.5}{11}}
\newlabel{StatTable*se}{{2.5}{12}}
\@writefile{lof}{\contentsline {figure}{\numberline {2.4}{\ignorespaces Statistical errors in a demonstration Monte Carlo computation.}}{12}}
\@writefile{toc}{\contentsline {section}{\numberline {2.6}Error amplification and unstable algorithms}{12}}
\newlabel{Stab*se}{{2.6}{12}}
\newlabel{error_amp*se}{{2.4}{13}}
\@writefile{toc}{\contentsline {section}{\numberline {2.7}Condition number and ill conditioned problems}{14}}
\newlabel{Cond*se}{{2.7}{14}}
\newlabel{oneDk1*se}{{2.5}{14}}
\newlabel{kapDef*se}{{2.6}{14}}
\newlabel{oneDk2*se}{{2.7}{14}}
\@writefile{lof}{\contentsline {figure}{\numberline {2.5}{\ignorespaces \it  A code fragment in which roundoff error can lead to numbers that should be equal in exact arithmetic not being equal in floating point.}}{15}}
\newlabel{FloatingPointInequality*se}{{2.5}{15}}
\newlabel{k2*se}{{2.8}{15}}
\@writefile{toc}{\contentsline {section}{\numberline {2.8}Software tips}{15}}
\newlabel{Tips*se}{{2.8}{15}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.8.1}Floating point numbers are (almost) never equal}{15}}
\@writefile{lof}{\contentsline {figure}{\numberline {2.6}{\ignorespaces \it  A code fragment illustrating a pitfall of using a floating point variable to regulate a {\tt  while} loop.}}{16}}
\newlabel{floatLoopTest*se}{{2.6}{16}}
\@writefile{lof}{\contentsline {figure}{\numberline {2.7}{\ignorespaces \it  A code fragment using an integer variable to regulate the loop of Figure 2.6\hbox {}.}}{16}}
\newlabel{intLoopTest*se}{{2.7}{16}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.8.2}Plotting data curves}{16}}
\@writefile{lof}{\contentsline {figure}{\numberline {2.8}{\ignorespaces \it  Plots of the first $n$ Fibonacci numbers, linear scale on the left, log scale on the right}}{17}}
\newlabel{PlotScaling*se}{{2.8}{17}}
\@writefile{toc}{\contentsline {section}{\numberline {2.9}Further reading}{17}}
\@writefile{lof}{\contentsline {figure}{\numberline {2.9}{\ignorespaces \it  A code fragment using an integer variable to regulate the loop of Figure 2.6\hbox {}.}}{18}}
\newlabel{PlotScalingScript*se}{{2.9}{18}}
\@writefile{toc}{\contentsline {section}{\numberline {2.10}Exercises}{19}}
\newlabel{TF*se}{{1}{19}}
\newlabel{Fib*se}{{4}{20}}
\newlabel{fibEqn*se}{{2.9}{20}}
\newlabel{Binom*se}{{5}{20}}
\newlabel{E(k)*se}{{2.10}{21}}
\newlabel{day}{{6}{21}}
\@writefile{toc}{\contentsline {chapter}{\numberline {3}NumericalAnalysis}{23}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{na*na}{{3}{23}}
\newlabel{fullSeries*na}{{3.1}{23}}
\newlabel{truncSeries*na}{{3.2}{23}}
\@writefile{toc}{\contentsline {section}{\numberline {3.1}Software tips}{24}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.1}Write flexible and verifiable codes}{24}}
\newlabel{flexibleCode*na}{{3.1.1}{24}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.2}Report failures}{25}}
\newlabel{reportFailure*na}{{3.1.2}{25}}
\@writefile{toc}{\contentsline {section}{\numberline {3.2}Exercises}{25}}
\newlabel{BigIntegralProgram*na}{{1}{25}}