diff --git a/semester3/numcs/numcs-summary.pdf b/semester3/numcs/numcs-summary.pdf index a7b008f..0dc827a 100644 Binary files a/semester3/numcs/numcs-summary.pdf and b/semester3/numcs/numcs-summary.pdf differ diff --git a/semester3/numcs/numcs-summary.tex b/semester3/numcs/numcs-summary.tex index 33050fb..ef50843 100644 --- a/semester3/numcs/numcs-summary.tex +++ b/semester3/numcs/numcs-summary.tex @@ -133,6 +133,9 @@ Moral of the story: Use descriptive variable names and do NOT use $t$, $tt$, $tt \section{Numerische Quadratur} \input{parts/02_quadrature/00_introduction.tex} \input{parts/02_quadrature/01_equidistant-nodes.tex} +\input{parts/02_quadrature/02_non-equidistant/00_gauss.tex} +\input{parts/02_quadrature/02_non-equidistant/01_clenshaw-curtis.tex} +\input{parts/02_quadrature/03_adaptive.tex} \end{document} diff --git a/semester3/numcs/parts/02_quadrature/02_non-equidistant/00_gauss.tex b/semester3/numcs/parts/02_quadrature/02_non-equidistant/00_gauss.tex new file mode 100644 index 0000000..23fe3c0 --- /dev/null +++ b/semester3/numcs/parts/02_quadrature/02_non-equidistant/00_gauss.tex @@ -0,0 +1,10 @@ +\newsection +\subsection{Nicht äquidistante Stützstellen} +Alternativ zur Unterteilung des Intervalls können wir andere Quadraturpunkte erlauben + +\subsubsection{Gauss Quadratur} +In diesem Kapitel werden die Gewichte mit $b_1, b_2, \ldots, b_s$ und die Knoten auf unserem Referenzintervall, +welches hier $[0, 1]$ ist, mit $c_1, c_2, \ldots, c_s \in [0, 1]$ bezeichnet. + +% TODO: It would probably be a good idea to link the document together much better (and maybe create an index in the end?) +Wir möchten unsere Gewichte $b_i$ und Knoten $c_i$ so bestimmen, dass die Quadraturordnung maximal ist. diff --git a/semester3/numcs/parts/02_quadrature/02_non-equidistant/01_clenshaw-curtis.tex b/semester3/numcs/parts/02_quadrature/02_non-equidistant/01_clenshaw-curtis.tex new file mode 100644 index 0000000..176edeb --- /dev/null +++ b/semester3/numcs/parts/02_quadrature/02_non-equidistant/01_clenshaw-curtis.tex @@ -0,0 +1 @@ +\subsubsection{Clenshaw-Curtis Quadraturformel} diff --git a/semester3/numcs/parts/02_quadrature/03_adaptive.tex b/semester3/numcs/parts/02_quadrature/03_adaptive.tex new file mode 100644 index 0000000..e41dac5 --- /dev/null +++ b/semester3/numcs/parts/02_quadrature/03_adaptive.tex @@ -0,0 +1,2 @@ +\newsection +\subsection{Adaptive Quadratur}