12 files changed, 1237 insertions, 19 deletions

diff --git a/skripti/365_prenesi_omejene_vsebine.sh b/skripti/365_prenesi_omejene_vsebine.sh
index f9a8c69..510b0c1 100755
--- a/skripti/365_prenesi_omejene_vsebine.sh
+++ b/skripti/365_prenesi_omejene_vsebine.sh
@@ -7,13 +7,24 @@
 set -euo pipefail
 page=`curl --fail-with-body https://365.rtvslo.si/oddaja/dnevnik/92` # outputa preveč shita za set -x
 set -x
-for id in `find -type f -size 7931523c | sed -E 's/^.*\[([0-9]*)\].*$/\1/g'` # repair broken downloads (pravice potekle)
-do
-	yt-dlp --no-continue http://365.rtvslo.si/arhiv/oddaja/$id
+find . -size -12M -type f -name '*.mp4' | while read file
+do # grep for specific audio codec ... if sample rate is 44100 and (tv broadcast is at 48000) and smaller than 12M, it's most likely the dummy/pravicepotekle video
+	samplerate=`ffprobe "$file" 2>&1 | grep 0x6134706D | grep -Eo '[0-9]+ Hz' | cut -d\  -f1`
+	id=`grep -Eo "\[[0-9]+\]\.mp" <<<"$file" | grep -o '[0-9]*'`
+	if [ $samplerate -eq 48000 ]
+	then
+		continue
+	fi
+	if [ $samplerate -eq 44100 ]
+	then
+		yt-dlp --no-continue http://365.rtvslo.si/arhiv/oddaja/$id # retry fu*ked up downloads
+		continue
+	fi
+	echo -e "Subject: unknown samplerate in 365.sh\n\nVideo file: $file\nsamplerate: $samplerate\n" | sendmail root
 done
 rm -f Error\ \[*\].mp4 
 dnevnik_id=`grep href=./arhiv/dnevnik <<<"$page" | cut -d\" -f2 | cut -d/ -f4 | head -n1`
-client_id=`grep client-id <<<"$page" | cut -d\" -f2 | head -n1`
+client_id=`grep 'client-id="' <<<"$page" | head -n1 | sed -E 's/^.*client-id="([^"]*)".*$/\1/'`
 if [ ! -f zadnji ]
 then
 	echo $dnevnik_id > zadnji
diff --git a/skripti/completion.bash b/skripti/completion.bash
new file mode 100644
index 0000000..fbe834d
--- /dev/null
+++ b/skripti/completion.bash
@@ -0,0 +1,6 @@
+# completion skript za vse stvari v /skripti/
+_service_sh_complete() {
+	[ $1 = $3 ] && { COMPREPLY=($(compgen -W "`service.sh list`" $2)); return; }
+	COMPREPLY=($(compgen -W "`service.sh $3 list`" $2))
+}
+complete -F _service_sh_complete service.sh
diff --git a/skripti/earhorn_m3u.sh b/skripti/earhorn_m3u.sh
index 51f33c7..e89a151 100755
--- a/skripti/earhorn_m3u.sh
+++ b/skripti/earhorn_m3u.sh
@@ -1,6 +1,19 @@
 #!/bin/bash
-set -xeo pipefail
+set -eo pipefail
+# $1 je prefix
+# $2 je prejšnji file (za caching dolžin)
+# $3=1 forsira cache kljub version failu
 echo "#EXTM3U"
+ver="#earhorn_m3u.sh različica 0"
+echo $ver
+cache=0
+if [ ! x$3 = x ] || [ ! x$2 = x ] && [ -f $2 ]
+then
+	if [ x"`head -n2 $2 | tail -n1`" = x"$ver" ]
+	then
+		cache=1
+	fi
+fi
 find 2* -type f | while read file
 do
 	date=`cut -d/ -f1,2,3 <<<$file | sed s,/,-,g`
@@ -8,7 +21,13 @@ do
 	h=${time:0:2}
 	m=${time:2:2}
 	s=${time:4:2}
-	echo "#EXTINF:`ffprobe -v error -show_entries format=duration -of default=noprint_wrappers=1:nokey=1 $file  | cut -d. -f1`,Radijski arhiv"
+	dol=""
+	if [ $cache -eq 1 ]
+	then
+		grep -B2 ^$1$file$ $2 && continue
+	fi
+	dol=`ffprobe -v error -show_entries format=duration -of default=noprint_wrappers=1:nokey=1 $file | cut -d. -f1`
+	echo "#EXTINF:$dol,Radijski arhiv"
 	echo "#EXT-X-PROGRAM-DATE-TIME:${date}T$h:$m:${s}Z"
 	echo $1$file
 done
diff --git a/skripti/init_script_interpreter.sh b/skripti/init_script_interpreter.sh
new file mode 100755
index 0000000..fc461ce
--- /dev/null
+++ b/skripti/init_script_interpreter.sh
@@ -0,0 +1,115 @@
+#!/bin/bash
+set -eo pipefail
+name=`rev <<<$1 | cut -d/ -f1 | rev`
+SVCNAME=$name
+pidfile=/run/user/`id -u`/$name.pid
+[ -w /run/user/`id -u`/log ] && stdout_logger="logger --socket /run/user/`id -u`/log" || stdout_logger=logger # failback to logging to syslog
+stderr_logger=$stdout_logger
+[ -r `sed s,/init.d/,/conf.d/, <<<$1` ] && . `sed s,/init.d/,/conf.d/, <<<$1`
+. $1
+type eerror > /dev/null 2> /dev/null || eerror() {
+	echo NAPAKA: $@
+}
+type ewarn > /dev/null 2> /dev/null || ewarn() {
+	echo OPOZORILO: $@
+}
+type einfo > /dev/null 2> /dev/null || einfo () {
+	echo INFO: $@
+}
+type ebegin > /dev/null 2> /dev/null || ebegin() {
+	echo ZAČENJAM: $@
+}
+type need_net > /dev/null 2> /dev/null || need_net() {
+	[ `ip a | grep ^[[:digit:]] | wc -l` -gt 1 ] || { eerror "Ni omrežnih vmesnikov poleg lo." && return 1; }
+	[ `ip route | wc -l` -gt 1 ] || { eerror "Usmerjevalna tabela je prazna." && return 1; }
+}
+type need_clock > /dev/null 2> /dev/null || need_clock() {
+	year=`date +%Y`
+	[ $? -eq 0 ] || { eerror "Ura ne deluje." && return 1; }
+	[ $year -ge 2024 ] || { eerror "Ura je narobe nastavljena." && return 1; }
+}
+type need_hostname > /dev/null 2> /dev/null || need_hostname() {
+	hn=`hostname`
+	[ $? -eq 0 ] || { eerror "Ni mogoče pridobiti imena gostitelja." && return 1; }
+	[ x$hn = x ] && { eerror "Ni imena gostitelja" && return 1; }
+	[ x$hn = xlocalhost ] && { eerror "Ime gostitelja je localhost." && return 1; }
+	return 0
+}
+needs=
+needs_izpolnjen=0
+type need > /dev/null 2> /dev/null || need() {
+	for i in $@
+	do
+		needs="$needs $i"
+		need_$i || { eerror "Odvisnost $i ni izpolnjena." && needs_izpolnjen=1; }
+	done
+}
+provides=
+type provide > /dev/null 2> /dev/null || provide() {
+	for i in $@
+	do
+		provides="$provides $i"
+	done
+}
+type depend > /dev/null 2> /dev/null || depend() {
+	return
+}
+type check_dependencies > /dev/null 2> /dev/null || check_dependencies() {
+	depend
+	return $needs_izpolnjen
+}
+type needs > /dev/null 2> /dev/null || needs() {
+	depend
+	echo $needs
+}
+type provides > /dev/null 2> /dev/null || provides() {
+	depend
+	echo $provides
+}
+type checkconfig > /dev/null 2> /dev/null || checkconfig() {
+	return
+}
+type start > /dev/null 2> /dev/null || start() {
+	checkconfig || { eerror "Checkconfig ni uspel." && return 1; };
+	check_dependencies || { eerror "Odvisnosti niso izpolnjene."; return 1; }
+	ebegin "Zaganjam $SVCNAME"
+	start-stop-daemon --start --verbose `[ x$command_background = true ] || echo --background --make-pidfile` `[ x$chdir = x ] || echo --chdir $chdir` --stdout-logger "$stdout_logger" --stderr-logger "$stderr_logger" --exec $command --pidfile $pidfile -- $command_args || { eerror "start-stop-daemon ni uspel. Koda napake: $?"; return 1; }
+}
+type stop > /dev/null 2> /dev/null || stop() {
+	ebegin "Ustavljam $SVCNAME"
+	start-stop-daemon --stop --pidfile $pidfile --verbose --exec $command -- $command_args || { eerror "start-stop-daemon ni uspel. Koda napake: $?"; return 1; }
+}
+type restart > /dev/null 2> /dev/null || restart() {
+	checkconfig || { eerror "Checkconfig ni uspel." && return 1; };
+	stop || ewarn "Stop ni uspel. Vseeno poskušam zagnati storitev."
+	start || { eerror "Start ni uspel." && return 1; }
+}
+type reload > /dev/null 2> /dev/null || reload() {
+	checkconfig || { eerror "Checkconfig ni uspel." && return 1; };
+	ebegin "Pošiljam SIGHUP storitvi $SVCNAME"
+	start-stop-daemon --signal HUP $start_stop_daemon_args
+}
+type status > /dev/null 2> /dev/null || status() {
+	if [ -r $pidfile ]
+	then
+		if [ -d /proc/`cat $pidfile` ]
+		then
+			einfo started
+		else
+			einfo crashed
+			return 3
+		fi
+	else
+		einfo stopped
+		return 3
+	fi
+}
+type list > /dev/null 2> /dev/null || list() {
+	echo start stop restart $extra_commands $extra_started_commands $extra_stopped_commands status reload list check_dependencies needs provides
+}
+if type $2 > /dev/null 2> /dev/null
+then
+	${@:2}
+else
+	eerror "Ta ukaz ne obstaja!"
+fi
diff --git a/skripti/service.sh b/skripti/service.sh
new file mode 100755
index 0000000..2617253
--- /dev/null
+++ b/skripti/service.sh
@@ -0,0 +1,28 @@
+#!/bin/bash
+[ x$INITPATH = x ] && for i in `tr : ' ' <<<$MORE_INITPATH` `tr : ' ' <<<$XDG_CONFIG_DIRS` ~/.config ~ /etc
+do
+	[ -d $i/init.d ] && INITPATH=$INITPATH:$i/init.d
+done
+if [ x$1 = xlist ]
+then
+	for i in `tr : ' ' <<<$INITPATH`
+	do
+		if [ -w $i ]
+		then
+			ls $i
+		else
+			for j in $i/*
+			do
+				[ ! -x $j ] && continue
+				head -n1 $j | grep "#!.*openrc-run" > /dev/null 2> /dev/null && continue
+				echo `rev <<<$j | cut -f/ -d1 | rev`
+			done
+		fi
+	done
+	exit 1
+fi
+[ x$1 = x ] && { echo -e "Uporaba:\n\t$0 list\n\t$0 <storitev> <dejanje>"; exit 1; }
+for i in `tr : ' ' <<<$INITPATH`
+do
+	[ -x $i/$1 ] && exec $i/$@
+done
diff --git a/skripti/videonadzor.sh b/skripti/videonadzor.sh
index 3e6fa51..e097c58 100755
--- a/skripti/videonadzor.sh
+++ b/skripti/videonadzor.sh
@@ -22,7 +22,7 @@ do
 		do
 			if [ $prev = devica ]
 			then
-				first=$i
+				first=`rev <<<"$i" | cut -d. -f2- | rev`
 				prev=$i
 				continue
 			fi
@@ -36,7 +36,7 @@ do
 			prev=$i
 		done
 		{
-			ffmpeg -f concat -safe 0 -i concat.txt -fps_mode vfr file:$first.mkv
+			ffmpeg -f concat -safe 0 -i concat.txt -vsync vfr file:$first.mkv
 			if [ -s $first.mkv ]
 			then
 				while read line
@@ -44,8 +44,8 @@ do
 					grep ^file <<<$line > /dev/null && rm `cut -d: -f2- <<<$line | cut -d\' -f1`
 				done < concat.txt
 			fi
-			oldstart=`ls --sort=time | grep mkv$ | tail -f1 | cut -d: -f1`
-			if [ ! $oldstart = `cut -d: -f1` <<<"$t" ]
+			oldstart=`ls --sort=time | grep mkv$ | tail -n1 | cut -d: -f1`
+			if [ ! $oldstart = `cut -d: -f1 <<<"$t"` ]
 			then
 				echo "ffconcat version 1.0" > concat.txt
 				prev=devica
@@ -63,7 +63,7 @@ do
 					fi
 					prev=$i
 				done
-				ffmpeg -f concat -safe 0 -i concat.txt -fps_mode vfr file:$oldstart.mp4
+				ffmpeg -f concat -safe 0 -i concat.txt -vsync vfr file:$oldstart.mp4
 				if [ -s $oldstart.mp4 ]
 				then
 					while read line
diff --git a/skripti/zone/axfr.py b/skripti/zone/axfr.py
index fe508f1..11eaad9 100755
--- a/skripti/zone/axfr.py
+++ b/skripti/zone/axfr.py
@@ -20,8 +20,8 @@ for naslov in naslovi: # opcijsko dodaj tule kakšen try catch
 		break
 config = None
 try:
-	config = json.loads(b''.join(dns.resolver.resolve("_urejevalnik." + domena, "TXT")[0].strings).decode())
-except dns.resolver.NXDOMAIN:
+	config = json.loads(b''.join(zone["_urejevalnik"].get_rdataset(dns.rdataclass.IN, dns.rdatatype.TXT)[0].strings).decode())
+except KeyError:
 	pass
 except json.decoder.JSONDecodeError:
 	pass
@@ -53,7 +53,8 @@ for r in zone.iterate_rdatas():
 		konec = config["i"][r[0].to_unicode()]
 	print(r[0].to_unicode(), end=konec)
 	if r[1] != config["t"]:
-		print(r[1], end="\t")
+		print(r[1], end="")
+	print("\t", end="")
 	if r[2].rdclass != dns.rdataclass.IN:
 		print(r[2].rdataclass.name, end="\t")
 	print(r[2].rdtype.name, end="\t")
diff --git a/skripti/zone/update.py b/skripti/zone/update.py
index 34a4e39..ead2c39 100755
--- a/skripti/zone/update.py
+++ b/skripti/zone/update.py
@@ -24,8 +24,8 @@ for naslov in naslovi: # opcijsko dodaj tule kakšen try catch
 		break
 config = None
 try:
-	config = json.loads(b''.join(dns.resolver.resolve("_urejevalnik." + domena, "TXT")[0].strings).decode())
-except dns.resolver.NXDOMAIN:
+	config = json.loads(b''.join(zone["_urejevalnik"].get_rdataset(dns.rdataclass.IN, dns.rdatatype.TXT)[0].strings).decode())
+except KeyError:
 	pass
 except json.decoder.JSONDecodeError:
 	pass
@@ -61,7 +61,7 @@ for r in zone.iterate_rdatas():
 			vrednost = '"' + niz + '"'
 	else:
 		vrednost = r[2].to_text()
-	rrs.append((r[1], r[0].to_unicode(), komentar, konec, r[2].rdclass, r[2].rdtype, vrednost))
+	rrs.append((r[1], r[0].to_unicode(), komentar, None, r[2].rdclass, r[2].rdtype, vrednost))
 komentar = ""
 lineno = 1
 novikomentarji = {}
@@ -118,7 +118,7 @@ while True:
 			except dns.rdatatype.UnknownRdatatype:
 				pass
 		if tip == None:
-			print(f"NAPAKA: na vrstici {lineno} ne najdem tipa zapisa. Vrstica je lahko bodisi komentar, ki se začne z ';', bodisi je v obliki IME [TTL={newconfig["t"]}] [CLASS=IN] TIP PODATKI.")
+			print(f"NAPAKA: na vrstici {lineno} ne najdem tipa zapisa. Vrstica je lahko bodisi komentar, ki se začne z ';', bodisi je v obliki IME [TTL={newconfig['t']}] [CLASS=IN] TIP PODATKI.")
 			print(f"Vsebina neveljavne vrstice: " + line)
 			sys.exit(1)
 		while line[datastart] in [" ", "\t"]:
@@ -133,7 +133,7 @@ while True:
 			data = data.split()
 			data[2] = str(int(data[2])+newconfig["+"])
 			data = " ".join(data)
-		tapl = (ttl, ime, komentar, konec, razred, tip, data)
+		tapl = (ttl, ime, komentar, None, razred, tip, data)
 		if komentar != "":
 			novikomentarji[ime + " " + tip.to_text(tip)] = komentar
 		if konec != "\t":
diff --git a/šola/ana2/fja.scad b/šola/ana2/fja.scad
new file mode 100644
index 0000000..4d18a17
--- /dev/null
+++ b/šola/ana2/fja.scad
@@ -0,0 +1,13 @@
+echo(version=version());
+function sinh(x) = (exp(1)-exp(-x))/2;
+function f(x, y, z) = sinh(z)*sinh(y)-sin(x);
+epsilon = 0.01;
+rob = 1;
+korak = 0.1;
+particle = 0.1;
+for (x = [-rob : korak : rob])
+    for (y = [-rob : korak : rob])
+        for (z = [-rob : korak : rob])
+            if (f(x, y, z) < epsilon)
+                translate([x, y, z])
+                    cube(particle);
\ No newline at end of file
diff --git a/šola/ana2/kolokvij1.lyx b/šola/ana2/kolokvij1.lyx
new file mode 100644
index 0000000..a4f9569
--- /dev/null
+++ b/šola/ana2/kolokvij1.lyx
@@ -0,0 +1,976 @@
+#LyX 2.3 created this file. For more info see http://www.lyx.org/
+\lyxformat 544
+\begin_document
+\begin_header
+\save_transient_properties true
+\origin unavailable
+\textclass article
+\begin_preamble
+\usepackage{siunitx}
+\usepackage{pgfplots}
+\usepackage{listings}
+\usepackage{multicol}
+\usepackage{amsmath}
+\sisetup{output-decimal-marker = {,}, quotient-mode=fraction, output-exponent-marker=\ensuremath{\mathrm{3}}}
+\DeclareMathOperator{\g}{g}
+\DeclareMathOperator{\sled}{sled}
+\DeclareMathOperator{\Aut}{Aut}
+\DeclareMathOperator{\Cir}{Cir}
+\DeclareMathOperator{\ecc}{ecc}
+\DeclareMathOperator{\rad}{rad}
+\DeclareMathOperator{\diam}{diam}
+\newcommand\euler{e}
+\end_preamble
+\use_default_options true
+\begin_modules
+enumitem
+\end_modules
+\maintain_unincluded_children false
+\language slovene
+\language_package default
+\inputencoding auto
+\fontencoding global
+\font_roman "default" "default"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_osf false
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures true
+\graphics xetex
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry true
+\use_package amsmath 1
+\use_package amssymb 1
+\use_package cancel 1
+\use_package esint 1
+\use_package mathdots 1
+\use_package mathtools 1
+\use_package mhchem 1
+\use_package stackrel 1
+\use_package stmaryrd 1
+\use_package undertilde 1
+\cite_engine basic
+\cite_engine_type default
+\biblio_style plain
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\justification false
+\use_refstyle 1
+\use_minted 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\leftmargin 1cm
+\topmargin 1cm
+\rightmargin 1cm
+\bottommargin 2cm
+\headheight 1cm
+\headsep 1cm
+\footskip 1cm
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style german
+\dynamic_quotes 0
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+setlength{
+\backslash
+columnseprule}{0.2pt}
+\backslash
+begin{multicols}{2}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Podmnožice v evklidskih prostorih
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $A$
+\end_inset
+
+ zaprta, če 
+\begin_inset Formula $\forall$
+\end_inset
+
+ zaporedje s členi v 
+\begin_inset Formula $A:$
+\end_inset
+
+ vsa stekališča v 
+\begin_inset Formula $A$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $A$
+\end_inset
+
+ kompaktna, če 
+\begin_inset Formula $\forall$
+\end_inset
+
+ zaporedje s členi v 
+\begin_inset Formula $A$
+\end_inset
+
+:
+\begin_inset Formula $\exists$
+\end_inset
+
+ stekališče v 
+\begin_inset Formula $A$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $f$
+\end_inset
+
+ je kompozitum zveznih 
+\begin_inset Formula $\Rightarrow$
+\end_inset
+
+ 
+\begin_inset Formula $f$
+\end_inset
+
+ zvezna
+\end_layout
+
+\begin_layout Standard
+za 
+\begin_inset Formula $x\in\mathbb{R}^{k}$
+\end_inset
+
+: 
+\begin_inset Formula $\text{\left|\left|x\right|\right|\ensuremath{\coloneqq}}\sqrt{x_{1}^{2}+\cdots+x_{k}^{2}}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $A\subseteq\mathbb{R}^{k}$
+\end_inset
+
+ omejena 
+\begin_inset Formula $\Leftrightarrow\exists M\in\mathbb{R}\forall x\in A:\left|\left|x\right|\right|<M$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $K\left(s\in\mathbb{R}^{k},M\in\mathbb{R}\right)\coloneqq\left\{ s+x\in\mathbb{R}^{k};\text{\left|\left|x\right|\right|}<M\right\} $
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $x\in A$
+\end_inset
+
+ notranja 
+\begin_inset Formula $\Leftrightarrow\exists\varepsilon\ni:K\left(x,\varepsilon\right)\subset A$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $A\subseteq\mathbb{R}^{k}$
+\end_inset
+
+ odprta 
+\begin_inset Formula $\Leftrightarrow\forall x\in A:x$
+\end_inset
+
+ notranja
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $A\subseteq\mathbb{R}^{k}$
+\end_inset
+
+ zaprta 
+\begin_inset Formula $\Leftrightarrow\mathbb{R}^{k}\setminus A$
+\end_inset
+
+ odprta
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $x\in\mathbb{R}^{k}$
+\end_inset
+
+ stekališče 
+\begin_inset Formula $A\Leftrightarrow\forall\varepsilon>0:K\left(x,\varepsilon\right)\cup\left(A\setminus\left\{ x\right\} \right)\not=\emptyset$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $x\in\mathbb{R}^{k}$
+\end_inset
+
+ izolirana točka 
+\begin_inset Formula $A\Leftrightarrow x$
+\end_inset
+
+ ni stekališče 
+\begin_inset Formula $A$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Zaporedje 
+\begin_inset Formula $a_{n}:\mathbb{N}\to\mathbb{R}^{k}$
+\end_inset
+
+ konvergira proti 
+\begin_inset Formula $a\in\mathbb{R}^{k}$
+\end_inset
+
+ kadar 
+\begin_inset Formula $\forall\varepsilon>0\exists N\in\mathbb{N}\forall n>N:\left|\left|a_{n}-a\right|\right|<\varepsilon$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $s\in\mathbb{R}^{k}$
+\end_inset
+
+ stekališče zap.
+ 
+\begin_inset Formula $\Leftrightarrow$
+\end_inset
+
+ v 
+\begin_inset Formula $\text{\ensuremath{\varepsilon}}-$
+\end_inset
+
+okolici 
+\begin_inset Formula $s$
+\end_inset
+
+ je 
+\begin_inset Formula $\infty$
+\end_inset
+
+mnogo členov
+\end_layout
+
+\begin_layout Standard
+Vsako omejeno zaporedje ima stekališče.
+\end_layout
+
+\begin_layout Section
+Funkcije več spremenljivk
+\end_layout
+
+\begin_layout Standard
+fja 
+\begin_inset Formula $k$
+\end_inset
+
+ spremenljivk je preslikava 
+\begin_inset Formula $f:D\subseteq\mathbb{R}^{k}\to\mathbb{R}$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $L\in\mathbb{R}$
+\end_inset
+
+ je limita 
+\begin_inset Formula $f:D\subseteq\text{\ensuremath{\mathbb{R}^{k}}}\to\mathbb{R}$
+\end_inset
+
+ v stekališču 
+\begin_inset Formula $a\in D$
+\end_inset
+
+, če 
+\begin_inset Formula $\forall\varepsilon>0\exists\delta>0\forall x\in D\setminus\left\{ a\right\} :\left|\left|x-a\right|\right|<\delta\Rightarrow\left|f\left(x\right)-L\right|<\varepsilon$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $\lim_{x\to a}\left(f\oslash g\right)x=\lim_{x\to a}fx\oslash\lim_{x\to a}gx$
+\end_inset
+
+, če obstajata.
+ 
+\begin_inset Formula $\oslash\in\left\{ +,-,\cdot\right\} $
+\end_inset
+
+.
+ 
+\begin_inset Formula $\oslash$
+\end_inset
+
+ je lahko deljenje, kadar 
+\begin_inset Formula $\lim_{x\to a}gx\not=0$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $f$
+\end_inset
+
+ zvezna v 
+\begin_inset Formula $a\Leftrightarrow\forall\varepsilon\exists\delta\forall x\in D:\left|\left|x-a\right|\right|<\delta\Rightarrow\left|fx-fa\right|<\varepsilon$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $f$
+\end_inset
+
+ zvezna 
+\begin_inset Formula $\Leftrightarrow\forall a\in D:f$
+\end_inset
+
+ zvezna v 
+\begin_inset Formula $a$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $f$
+\end_inset
+
+ zvezna v stekališču 
+\begin_inset Formula $a\Leftrightarrow\lim_{x\to a}fx=fa$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $A\subseteq\mathbb{R}^{k}$
+\end_inset
+
+ kompaktna, 
+\begin_inset Formula $f:A\to\mathbb{R}$
+\end_inset
+
+ zvezna
+\begin_inset Formula $\Rightarrow f$
+\end_inset
+
+ omejena in doseže maksimum in minimum (obstoj globalnega ekstrema).
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $f,g$
+\end_inset
+
+ zv.
+ 
+\begin_inset Formula $\Rightarrow f\oslash g$
+\end_inset
+
+ zv.
+ 
+\begin_inset Formula $\oslash\in\left\{ +,-,\cdot,\circ\right\} ,\oslash=/\Leftrightarrow\forall x:gx\not=0$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Odvodi funkcij več spremenljivk
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $f_{x_{i}}a$
+\end_inset
+
+, 
+\begin_inset Formula $i\in\left\{ 1..k\right\} $
+\end_inset
+
+ je odvod fje 
+\begin_inset Formula $x_{i}\to f\left(a_{1},\dots,a_{i-1},x_{i},a_{i+1},\dots,a_{k}\right)$
+\end_inset
+
+ v točki 
+\begin_inset Formula $a_{i}$
+\end_inset
+
+.
+ 
+\begin_inset Formula $f_{x_{i}}a=\lim_{x_{i}\to a_{i}}\frac{f\left(a_{1},\dots,a_{i-1},x_{i},a_{i+1},\dots,a_{k}\right)-fa}{x_{i}-a_{i}}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Tang.
+ ravn.
+ v 
+\begin_inset Formula $a=\left(b,c\right)$
+\end_inset
+
+
+\begin_inset Formula $a=\left(b,c\right)$
+\end_inset
+
+: 
+\begin_inset Formula $z=fa+f_{x}a\cdot\left(x-b\right)+f_{y}a\cdot\left(y-c\right)$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $f$
+\end_inset
+
+ je odvedljiva v 
+\begin_inset Formula $a\Leftrightarrow\lim_{h\to\left(0,0\right)}\frac{R_{a}\left(a+h\right)}{\left|\left|h\right|\right|}=0$
+\end_inset
+
+, kjer je 
+\begin_inset Formula $R_{a}\left(a+h\right)\coloneqq f\left(a+h\right)-fa-f_{x}\left(a\right)\cdot u+f_{y}\left(a\right)\cdot v$
+\end_inset
+
+ za 
+\begin_inset Formula $h=\left(u,v\right)$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $dfa\coloneqq\left[f_{x_{1}}a\cdots f_{x_{k}}a\right]=\nabla fa,dfa\cdot h\coloneqq f_{x_{1}}a\cdot h_{1}+\cdots+f_{x_{k}}a\cdot h_{k}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $f$
+\end_inset
+
+ v 
+\begin_inset Formula $a$
+\end_inset
+
+ odvedljiva 
+\begin_inset Formula $\Rightarrow f$
+\end_inset
+
+ v 
+\begin_inset Formula $a$
+\end_inset
+
+ zvezna
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $\forall i\in\left\{ 1..k\right\} :\exists f_{x_{i}}\wedge f_{x_{i}}$
+\end_inset
+
+ zvezna 
+\begin_inset Formula $\Rightarrow f$
+\end_inset
+
+ odvedljiva
+\end_layout
+
+\begin_layout Standard
+Lagrange: 
+\begin_inset Formula $fx_{1}-fx_{2}=f'\xi\left(x_{2}-x_{1}\right)$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $f\in C^{r}U\sim$
+\end_inset
+
+ 
+\begin_inset Formula $f$
+\end_inset
+
+ 
+\begin_inset Formula $r-$
+\end_inset
+
+krat zvezno odvedljiva v vsaki točki 
+\begin_inset Formula $U$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $f:U\subseteq\mathbb{R}^{k}\to\mathbb{R},f\in C^{2}U\Rightarrow\forall i,j\in\left\{ 1..k\right\} :f_{x_{i}}=f_{x_{j}}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $\frac{df}{d\vec{s}}\left(x,y\right)=\lim_{t\to0}\frac{f((x,y)+t\vec{s})-f(x,y)}{t}=s_{1}f(x,y)+s_{2}f_{x}(x,y)$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Tangentna ravnina v 
+\begin_inset Formula $\left(x_{0},y_{0},f\left(x_{0},y_{0}\right)\right)$
+\end_inset
+
+ je 
+\begin_inset Formula $f_{x}\left(x_{0},y_{0}\right)\left(x-x_{0}\right)+f_{y}\left(x_{0},y_{0}\right)\left(y-y_{0}\right)-z+f\left(x_{0},y_{0}\right)$
+\end_inset
+
+ in razpenjata jo vektorja 
+\begin_inset Formula $\left(1,0,f_{x}\right)$
+\end_inset
+
+ in 
+\begin_inset Formula $\left(0,1,f_{y}\right)$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Taylorjeva formula in verižno pravilo
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $f$
+\end_inset
+
+ diferenciabilna v 
+\begin_inset Formula $a\in\mathbb{R}^{k}\Rightarrow f\left(a+h\right)\cong fa+dfa\cdot h=fa+f_{x_{1}}a\cdot h_{1}+\cdots+f_{x_{k}}a\cdot h_{k}$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $U\subseteq R^{k}$
+\end_inset
+
+ odprta in 
+\begin_inset Formula $f:U\to\mathbb{R},f\in C^{n+1}U$
+\end_inset
+
+.
+ Naj bo 
+\begin_inset Formula $D_{f,r,a}$
+\end_inset
+
+ vektor vseh parcialnih odvodov reda 
+\begin_inset Formula $r$
+\end_inset
+
+ v točki 
+\begin_inset Formula $a$
+\end_inset
+
+.
+ Primer: 
+\begin_inset Formula $D_{f,2,a}=\left(f_{xx}a,2f_{xy}a+f_{yy}a\right)$
+\end_inset
+
+.
+ 
+\begin_inset Formula $D_{f,0,a}\coloneqq f\left(a\right)$
+\end_inset
+
+.
+ Naj bo 
+\begin_inset Formula $H_{r}$
+\end_inset
+
+ vektor z vsemi kombinacijami dolžine 
+\begin_inset Formula $r$
+\end_inset
+
+ komponent 
+\begin_inset Formula $h$
+\end_inset
+
+.
+ Primer: 
+\begin_inset Formula $H_{2}=\left(uu,2uv,vv\right)$
+\end_inset
+
+.
+ 
+\begin_inset Formula $H_{0}=1$
+\end_inset
+
+.
+ 
+\begin_inset Formula $D_{f,r,a}\cdot H_{r}$
+\end_inset
+
+ je njun skalarni produkt.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+T_{f,a,n}\left(h_{1}=x-a,h_{2}=y-b\right)=\sum_{i=0}^{n}\frac{1}{i!}\left(D_{f,i,a}\cdot H_{i}\right)
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Ekstremalni problemi
+\end_layout
+
+\begin_layout Standard
+Kandidati so 
+\begin_inset Formula $a$
+\end_inset
+
+, da 
+\begin_inset Formula $\nabla fa=0$
+\end_inset
+
+ ali 
+\begin_inset Formula $f$
+\end_inset
+
+ ni odv.
+ v 
+\begin_inset Formula $a$
+\end_inset
+
+ ali 
+\begin_inset Formula $a$
+\end_inset
+
+ robna točka.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+H\left(a,b\right)=\left[\begin{array}{cc}
+f_{xx}\left(a,b\right) & f_{xy}\left(a,b\right)\\
+f_{yx}\left(a,b\right) & f_{yy}\left(a,b\right)
+\end{array}\right]
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $\det H\left(a,b\right)>0$
+\end_inset
+
+: 
+\begin_inset Formula $f_{xx}\left(a,b\right)>0$
+\end_inset
+
+ l.
+ min., 
+\begin_inset Formula $f_{xx}\left(a,b\right)<0$
+\end_inset
+
+ l.
+ max.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $\det H\left(a,b\right)<0$
+\end_inset
+
+ sedlo
+\end_layout
+
+\begin_layout Standard
+Izrek o implicitni funkciji: 
+\begin_inset Formula $D\subseteq\mathbb{R}^{2}$
+\end_inset
+
+ odprta, 
+\begin_inset Formula $f:D\to\mathbb{R}$
+\end_inset
+
+ zvezno parcialno odvedljiva.
+ 
+\begin_inset Formula $K=\left\{ \left(x,y\right)\in D;f\left(x,y\right)=0\right\} $
+\end_inset
+
+.
+ Za 
+\begin_inset Formula $\left(a,b\right)\in D$
+\end_inset
+
+, 
+\begin_inset Formula $f\left(a,b\right)=0\wedge\nabla f\left(a,b\right)\not=0\exists h\left(a\right)=b,f\left(x,h\left(x\right)\right)=0\forall x\in U$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Vezani ekstrem: 
+\begin_inset Formula $D^{\text{odp.}}\subseteq\mathbb{R}^{n}$
+\end_inset
+
+, 
+\begin_inset Formula $f:D\to\mathbb{R}$
+\end_inset
+
+ diferenciabilna na 
+\begin_inset Formula $D$
+\end_inset
+
+.
+ let 
+\begin_inset Formula $g:D\to\mathbb{R}$
+\end_inset
+
+ zvezno parcialno odvedljiva, 
+\begin_inset Formula $A\coloneqq\left\{ x\in D;gx=0\right\} $
+\end_inset
+
+.
+ 
+\begin_inset Formula $\exists$
+\end_inset
+
+ vezani ekstrem 
+\begin_inset Formula $f$
+\end_inset
+
+ pri pogoju 
+\begin_inset Formula $g\Leftrightarrow\nabla fa=\lambda\nabla ga$
+\end_inset
+
+.
+ Kandidati za vezane ekstreme so stac.
+ točke fje 
+\begin_inset Formula $F\left(x,\lambda\right)=fx-\lambda gx$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Krivulje in ploskve
+\end_layout
+
+\begin_layout Standard
+Pot v 
+\begin_inset Formula $\mathbb{R}^{3}\sim\vec{r}:I\to\mathbb{R}^{3},I\in\mathbb{R}$
+\end_inset
+
+ interval.
+ 
+\begin_inset Formula $\forall t\in I:\vec{r}t=\left(xt,yt,zt\right)$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Odvod poti: 
+\begin_inset Formula $\dot{\vec{r}}\left(t\right)=\left(\dot{x}\left(t\right),\dot{y}\left(t\right),\dot{z}\left(t\right)\right)$
+\end_inset
+
+.
+ 
+\begin_inset Formula $\dot{\vec{r}}t$
+\end_inset
+
+ je tangentni vektor na krivuljo v točki 
+\begin_inset Formula $\vec{r}t$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Dolžina poti 
+\begin_inset Formula $\vec{r}:\left[a,b\right]\to\mathbb{R}^{3}$
+\end_inset
+
+ je 
+\begin_inset Formula 
+\[
+L=\int_{a}^{b}\left|\dot{\vec{r}}t\right|dt=\int_{a}^{b}\sqrt{\dot{x}^{2}t+\dot{y}^{2}t}dt
+\]
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Ploščina območja, ki ga omejuje krivulja, če je parametrizacija taka, da
+ je krivulja levo od 
+\begin_inset Formula $\vec{r}t$
+\end_inset
+
+: 
+\begin_inset Formula $\text{Pl\left(D\right)=\ensuremath{\frac{1}{2}\int_{a}^{b}\left(xt\dot{y}t-\dot{x}tyt\right)dt}}$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Ploskev eksplicitno kot graf 
+\begin_inset Formula $f:D^{\text{odp.}}\subseteq\mathbb{R}^{2}\to\mathbb{R}$
+\end_inset
+
+.
+ 
+\begin_inset Formula $f$
+\end_inset
+
+ difer.
+ v 
+\begin_inset Formula $\left(x,y\right)\Rightarrow$
+\end_inset
+
+ v 
+\begin_inset Formula $\left(x,y,f\left(x,y\right)\right)$
+\end_inset
+
+ definiramo tangentno ravnino z normalo 
+\begin_inset Formula $\left(-f_{x}\left(x,y\right),-f_{y}\left(x,y\right),1\right)$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Ploskev implicitno: 
+\begin_inset Formula $f:\mathbb{R}^{3}\to\mathbb{R}$
+\end_inset
+
+ zvezno parcialno odvedljiva.
+\begin_inset Formula 
+\[
+P=\left\{ \left(x,y,z\right)\in\mathbb{R}^{3};f\left(x,y,z\right)=0\right\} 
+\]
+
+\end_inset
+
+Če 
+\begin_inset Formula $\forall\left(x,y,z\right)\in P:\nabla f\left(x,y,z\right)\not=0\Rightarrow P$
+\end_inset
+
+ ploskev v 
+\begin_inset Formula $\mathbb{R}^{3}$
+\end_inset
+
+, saj je po izreku o implicitni fji 
+\begin_inset Formula $P$
+\end_inset
+
+ lokalno graf fje dveh spremenljivk.
+ Normala tangentne ravnine v 
+\begin_inset Formula $\left(x,y,z\right)\in P$
+\end_inset
+
+ ima normalo 
+\begin_inset Formula $\nabla f\left(x,y,z\right)$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+end{multicols}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
diff --git a/šola/p2/dn/DN07a_63230317.c b/šola/p2/dn/DN07a_63230317.c
new file mode 100644
index 0000000..3bc5323
--- /dev/null
+++ b/šola/p2/dn/DN07a_63230317.c
@@ -0,0 +1,25 @@
+#include <stdio.h>
+#include <stdlib.h>
+int globina (int * t) {
+	fprintf(stderr, "-> %d %d\n", t[0], t[1]);
+	if (!t[0] && !t[1])
+		return 0;
+	int r = 0;
+	if (t[0])
+		r = globina(t+2*t[0]);
+	if (t[1]) {
+		int g = globina(t+2*t[1]);
+		if (g > r)
+			r = g;
+	}
+	return r+1;
+		
+}
+int main (void) {
+	int n;
+	scanf("%d\n", &n);
+	int t[2*n];
+	for (int i = 0; i < 2*n; i++)
+		scanf("%d", &t[i]);
+	printf("%d\n", globina(t));
+}
diff --git a/šola/p2/dn/DN07b_63230317.c b/šola/p2/dn/DN07b_63230317.c
new file mode 100644
index 0000000..72a1ee9
--- /dev/null
+++ b/šola/p2/dn/DN07b_63230317.c
@@ -0,0 +1,24 @@
+#include <stdio.h>
+#include <stdbool.h>
+#include <string.h>
+int main (void) {
+	int n = 0;
+	scanf("%d\n", &n);
+	char nizi[n][43];
+	int offseti[n];
+	memset(offseti, 0, n*sizeof offseti[0]);
+	for (int i = 0; i < n; i++)
+		gets(nizi[i]); // izziv je v domačih nalogah pisat čim bolj nevarno a vseeno standardno C kodo
+	while (true) {
+		for (int i = 0; i < n; i++)
+			putchar(nizi[i][offseti[i]]);
+		putchar('\n');
+		offseti[n-1]++;
+		for (int i = n-1; !nizi[i][offseti[i]]; i--) {
+			offseti[i] = 0;
+			offseti[i-1]++;
+			if (!i)
+				return 0;
+		}
+	}
+}