From 6da7b66d5701b321518ac0dc25bd0ad2f6234b3e Mon Sep 17 00:00:00 2001 From: flavis Date: Thu, 25 Jun 2020 19:13:02 +0200 Subject: [PATCH] update ana8 and num7 --- sose2020/ana/lectures | 2 +- sose2020/ana/uebungen/ana8.pdf | Bin 125913 -> 125898 bytes sose2020/ana/uebungen/ana8.tex | 6 +++--- sose2020/num/uebungen/num7.pdf | Bin 126905 -> 126908 bytes sose2020/num/uebungen/num7.tex | 2 +- 5 files changed, 5 insertions(+), 5 deletions(-) diff --git a/sose2020/ana/lectures b/sose2020/ana/lectures index 01365dc..2ffc6c3 160000 --- a/sose2020/ana/lectures +++ b/sose2020/ana/lectures @@ -1 +1 @@ -Subproject commit 01365dc0b8fcf74c0861540ec715304fd6e958dd +Subproject commit 2ffc6c3ce9d68dd5b89540f31512321b8a3d278f diff --git a/sose2020/ana/uebungen/ana8.pdf b/sose2020/ana/uebungen/ana8.pdf index a4fc5ade387f238a75724b3fc4557df12db07b4c..da4856955abaae05c777b9632955439bb3d93fbd 100644 GIT binary patch delta 8146 zcmV;@A1&b7*9Xei2aqHJF*%cg9Vvet*={7a@m*ihejCAVnk*JC83N*suQjs4#ukDA 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3fc7e35..3f8e038 100644 --- a/sose2020/ana/uebungen/ana8.tex +++ b/sose2020/ana/uebungen/ana8.tex @@ -32,7 +32,7 @@ \end{proof} \item Beh.: Es ist mit $h = (h_1, h_2, h_3)^{T} \in \R^{3}$: \[ - T_{2}^{f}(\hat{x} + h) = -e\left(-h_1 - h_2 -h_3 + \frac{1}{2} h_2^2 + h_1 h_2 + h_1h_3\right) + T_{2}^{f}(\hat{x} + h) = -e\left(1 -h_1 - h_2 -h_3 + \frac{1}{2} h_2^2 + h_1 h_2 + h_1h_3\right) .\] \begin{proof} Mit $\hat{x} = (-1, -1, 0)^{T}$ folgt @@ -57,7 +57,7 @@ \begin{salign*} T_2^{f}(\hat{x} + h) &= f(\hat{x}) + (\nabla f(\hat{x}), h)_2 + \frac{1}{2} (H_f(\hat{x})h, h)_2 \\ &= -e + eh_1 + eh_2 + eh_3 - \frac{1}{2} eh_2^2 - eh_1h_2 - eh_1h_3 \\ - &= -e \left(-h_1 - h_2-h_3 + \frac{1}{2}h_2^2 + h_1h_2 + h_1 h_3\right) + &= -e \left(1 -h_1 - h_2-h_3 + \frac{1}{2}h_2^2 + h_1h_2 + h_1 h_3\right) .\end{salign*} \end{proof} \end{enumerate} @@ -170,7 +170,7 @@ $F(x,y)$ stetig partiell differenzierbar, da alle partiellen Ableitungen stetig sind. 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A_{11}A_{11}^{-1} & A_{21}A_{11}^{-1}A_{12} + S \end{pmatrix} = \begin{pmatrix} A_{11} & A_{12} \\