From 3bc264184b4e2783d5405dc32559751e82039fd4 Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Sun, 18 Jan 2026 08:12:00 +0100 Subject: [PATCH] [Analysis] Fix error --- .../analysis-ii-cheat-sheet.pdf | Bin 333196 -> 333363 bytes .../01_partial_derivatives.tex | 5 +++-- 2 files changed, 3 insertions(+), 2 deletions(-) diff --git a/semester3/analysis-ii/cheat-sheet-jh/analysis-ii-cheat-sheet.pdf b/semester3/analysis-ii/cheat-sheet-jh/analysis-ii-cheat-sheet.pdf index 3c415a8258c8cceed29efabd5529f3515c6423c4..12356f550c3211606972422f6c1deef373dded09 100644 GIT binary patch delta 28846 zcmV(#K;*xSs}!@W6tF=Ge<8n)j^M(CB7aGNRpn5J6u>eN3LS1y2@xxoML8W|DK6-z z#5#JDV9{|Oxt-k?598?1XS0WY5n=m^NoBhBfdkXph2c>(=qLCBQuR{FVfG`vKd$|1 zzYc?GPFFtKr&FJ;&a%6I)#|rw!%FXBSmeYpXM_n+ z^b7jYg;Q)gN0kOYX0PjdgKbGk3$#G1&F*D=On`t%Fz+h8r7)(d|;)G@f-`MN)> z)pi*Z=8MB>?<1#^R0FM2Wzhdgsm_n>ruNmo*&SHz8$7yA_B{(zWKEkX4r!9&Vz>Yq zJuuU(UEmX_VyNoxT>L5uwqHJ2k@D4+{jc|CdZJJ)23mkYM|-7{8y{@aUZ|MKrjEx4+rGGg)K4!?3M7mmA13ch%8 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zDp7s5=HI?V*ZqQI(Cc+T#Fynu_9!Jus`pvamMI`yNGK(S6+#10yvp1r?UMIP2PZ)M x7a;$CBL3|#|68zT`?jDRa#U>$_XE1P389w(hXqLl&&tEY4M#~SsVoKezW|(mp4I>W diff --git a/semester3/analysis-ii/cheat-sheet-jh/parts/vectors/differentiation/01_partial_derivatives.tex b/semester3/analysis-ii/cheat-sheet-jh/parts/vectors/differentiation/01_partial_derivatives.tex index 432061b..90e61e0 100644 --- a/semester3/analysis-ii/cheat-sheet-jh/parts/vectors/differentiation/01_partial_derivatives.tex +++ b/semester3/analysis-ii/cheat-sheet-jh/parts/vectors/differentiation/01_partial_derivatives.tex @@ -24,14 +24,15 @@ $\frac{\partial f}{\partial x_i}(x_0), \partial_{x_i} f(x_0) \text{ or } \partia and if $g(x) \neq 0 \smallhspace \forall x \in X$, then if $f \div g$ has $\partial_i$ on $X$, then so does $f \div g$ and $\partial_{x_i}(f \div g) = (\partial_{x_i}(f) g - f \partial_{x_i}(g)) \div g^2$\\ % ──────────────────────────────────────────────────────────────────── -\compactdef{Jacobi Matrix $J$} Element $J_ij = \partial_{x_j} f_i(x)$ for function $f: X \rightarrow \R^m$ with $X \subseteq \R^n$ open. $x_j$ is the $j$-th variable, +\compactdef{Jacobi Matrix $J$} Element $J_{ij} = \partial_{x_j} f_i(x)$ for function $f: X \rightarrow \R^m$ with $X \subseteq \R^n$ open. $x_j$ is the $j$-th variable, $f_i$ is the $i$-th component of the equation (i.e. in the vector of the function). $J$ has $m$ rows and $n$ columns.\\ % ──────────────────────────────────────────────────────────────────── \drmvspace\drmvspace \stepLabelNumber{all} \compactdef{Gradient, Divergence} for $f : X \rightarrow \R$ with $X \in \R^n$ open, the \bi{gradient} is given by -$\nabla f(x_0) = \begin{pmatrix} +$\nabla f(x_0) = + \begin{pmatrix} \partial_{x_1} f(x_0) \\ \vdots \\ \partial_{x_n} f(x_0)