\contentsline {section}{\numberline {1}Introduction}{1}{section.1}%
\contentsline {section}{\numberline {2}Some basic background material}{1}{section.2}%
\contentsline {section}{\numberline {3}Approximating differential equations on manifolds}{8}{section.3}%
\contentsline {subsection}{\numberline {3.1}A first attempt at a numerical approximation}{16}{subsection.3.1}%
\contentsline {subsection}{\numberline {3.2}Approximating the exponential map}{18}{subsection.3.2}%