\contentsline {part}{I\hspace {1em}Numerical methods}{1}{}%
\contentsline {chapter}{\numberline {1}Errors}{5}{}%
\contentsline {section}{\numberline {1.1}Roundoff error}{5}{}%
\contentsline {section}{\numberline {1.2}Approximation error}{6}{}%
\contentsline {section}{\numberline {1.3}Truncation error}{6}{}%
\contentsline {part}{II\hspace {1em}Interpolation and Approximation theory}{9}{}%
\contentsline {chapter}{\numberline {2}Interpolation}{11}{}%
\contentsline {section}{\numberline {2.1}Lagrange polynomial interpolation}{11}{}%
\contentsline {section}{\numberline {2.2}Vandermonde polynomial interpolation}{12}{}%
\contentsline {section}{\numberline {2.3}Spline interpolation}{13}{}%
\contentsline {chapter}{\numberline {3}Approximation theory}{15}{}%
\contentsline {section}{\numberline {3.1}Taylor series approximation}{15}{}%
\contentsline {section}{\numberline {3.2}Padé approximant}{15}{}%
\contentsline {section}{\numberline {3.3}Stirling's formula}{15}{}%
\contentsline {part}{III\hspace {1em}Numerical differentiation and integration}{17}{}%
\contentsline {chapter}{\numberline {4}Numerical differentiation}{19}{}%
\contentsline {section}{\numberline {4.1}Forward difference}{19}{}%
\contentsline {section}{\numberline {4.2}Backwards difference}{19}{}%
\contentsline {section}{\numberline {4.3}Balanced difference}{19}{}%
\contentsline {section}{\numberline {4.4}Higher order methods}{19}{}%
\contentsline {chapter}{\numberline {5}Numerical integration}{21}{}%
\contentsline {section}{\numberline {5.1}Riemann sum}{21}{}%
\contentsline {section}{\numberline {5.2}Trapezoidal rule}{21}{}%
\contentsline {section}{\numberline {5.3}Refined trapezoidal rule}{22}{}%
\contentsline {section}{\numberline {5.4}Romberg integration}{22}{}%
\contentsline {section}{\numberline {5.5}Simpson's rule}{22}{}%
\contentsline {chapter}{\numberline {6}Advanced methods}{23}{}%
\contentsline {section}{\numberline {6.1}Gauss-Legendre integration}{23}{}%
\contentsline {section}{\numberline {6.2}Monte Carlo integration}{24}{}%
\contentsline {part}{IV\hspace {1em}Numerical solutions to differential equation}{27}{}%
\contentsline {part}{V\hspace {1em}Root finding methods}{31}{}%
\contentsline {part}{VI\hspace {1em}Numerical solutions to systems of equations}{35}{}%
\contentsline {chapter}{\numberline {7}Power method}{39}{}%
\contentsline {chapter}{\numberline {8}Inverse power method}{41}{}%
\contentsline {chapter}{\numberline {9}QR iteration}{43}{}%
\contentsline {chapter}{\numberline {10}Arnoldi iteration}{45}{}%
\contentsline {part}{VII\hspace {1em}Numerical optimization}{47}{}%
\contentsline {section}{\numberline {10.1}Bracketing method}{49}{}%
\contentsline {section}{\numberline {10.2}Golden section search}{49}{}%
\contentsline {section}{\numberline {10.3}Jarratt's method}{49}{}%