From 1a58178ec862ead140e6518cd20cc223ef149a2e Mon Sep 17 00:00:00 2001 From: Erik Grobecker Date: Thu, 28 Nov 2024 19:53:33 +0100 Subject: [PATCH] alte ABs und sowas --- .pre-commit-config.yaml | 2 +- INDEX.md | 10 +- .../assets/bio_übungen-stammbaumanalyse.pdf | Bin 0 -> 261726 bytes schule/bio/bio_2024-11-21.typ | 134 ++++++++++++++---- schule/geschichte/assets/Geschichte Q2 5.pdf | Bin 0 -> 492416 bytes schule/mathe/other/funktionsuntersuchung.md | 83 +++++++++++ shell.nix | 2 + 7 files changed, 197 insertions(+), 34 deletions(-) create mode 100644 schule/bio/assets/bio_übungen-stammbaumanalyse.pdf create mode 100644 schule/geschichte/assets/Geschichte Q2 5.pdf create mode 100644 schule/mathe/other/funktionsuntersuchung.md diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml index 75c0898..b090596 100644 --- a/.pre-commit-config.yaml +++ b/.pre-commit-config.yaml @@ -1,5 +1,5 @@ repos: - repo: https://github.com/Enter-tainer/typstyle - rev: "v0.11.35" # The the revision or tag you want to use + rev: "v0.12.4" # The the revision or tag you want to use hooks: - id: typstyle diff --git a/INDEX.md b/INDEX.md index f6a7da6..e19fe59 100644 --- a/INDEX.md +++ b/INDEX.md @@ -14,12 +14,13 @@ Hier wird nach Fächern sortiert und für diese einzelne Tabellen erstellt. - [Spanisch](#spanisch) **TODOS:** + - [ ] Index beenden - [ ] Themen für alle Fächer angeben - [ ] weitere Themenfelder erfassen -> Orga & anderes - [x] zu PDFs statt `.typ` linken (ggf. Dokumente fixen) -- [ ] Export-Script schreiben (oder etwas über *pre-commit* finden) - - evtl. Etwas ähnlich wie das *quick-add* welches ich in Obsidian verwendet habe +- [ ] Export-Script schreiben (oder etwas über _pre-commit_ finden) + - evtl. Etwas ähnlich wie das _quick-add_ welches ich in Obsidian verwendet habe ## Biologie @@ -76,6 +77,10 @@ Hier wird nach Fächern sortiert und für diese einzelne Tabellen erstellt. | | 31.10.2024 | [hier](./schule/mathe/pdfs/MA_2024-10-31.pdf) | | **$e$-Funktionen**: Letzte Stunde vor der Klausur | 21.11.2024 | [hier](./schule/mathe/pdfs/MA_2024-11-21.pdf) | +Zusammenfassungen: + +- [Funktionsuntersuchungen](./schule/mathe/other/funktionsuntersuchung.md) + ## Philosophie | Thema | Datum | Link | @@ -104,4 +109,3 @@ Hier wird nach Fächern sortiert und für diese einzelne Tabellen erstellt. | ----- | ---------- | ---- | | | 05.11.2024 | | | | 11.11.2024 | | - diff --git a/schule/bio/assets/bio_übungen-stammbaumanalyse.pdf b/schule/bio/assets/bio_übungen-stammbaumanalyse.pdf new file mode 100644 index 0000000000000000000000000000000000000000..85ae1a6d4a1136e2a154208abee15c309746daec GIT binary patch literal 261726 zcmeFZ2Ut|ivM4%;ilTss2ojYXM1l-Cs3ZZ0;4tJMnPC`^Fyx^4OB4_gkc?!8BpHSz 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z&JPV#MPD9(08=v@OzAL8swE5wg#_DMI5(KY5m2zP_}UiSXmA-Eisk}(iN75JzrG60 zTtFMb2?Onc;s)@iTt7EPG(NZZcF4y^OcAqHF45X^$sM%!9P-`G|ktZM$Ug?6^& zV4!}{>2d>o7nr3mABZ^-0cNuZ(gA}Hf*WW>zG)qZzR}R%v?AYV$nTnxZ#3@jTC`mn z8v0#x^^FF@=pry5%-b=)2yQe`>it6F!lbgre7;==hQoKQ+}C^2Py}X&zvntok-ao9 zg!a}04dn6<_x`9oxn!+x58!7pS`4tk$EZ?(Ao&|r3X5JK;>E{IW97>)Gf#@?s#vf> lSg;vH4Fj^8=0CqJj + +**Funktionsuntersuchung** + +Die Funktionsuntersuchung dient dazu, den Verlauf und die Eigenschaften einer gegebenen Funktion $f(x)$ zu analysieren und zu beschreiben. Typische Aspekte einer Funktionsuntersuchung sind: + +1. **Definitionsmenge (D):** Bestimmung aller erlaubten x-Werte, für die die Funktion definiert ist. + + - _Beispiel:_ $f(x) = \frac{1}{x-2}$ hat die Definitionsmenge $D = \mathbb{R} \setminus \{2\}$, da der Nenner nicht Null sein darf. + +2. **Wertebereich (W):** Bestimmung aller möglichen y-Werte, die die Funktion annehmen kann. + + - _Beispiel:_ $f(x) = x^2$ hat den Wertebereich $W = [0, \infty)$, da Quadrate immer nicht-negativ sind. + +3. **Symmetrie:** + + - **Achsensymmetrie zur y-Achse:** Wenn $f(-x) = f(x)$ für alle $x \in D$. + - _Beispiel:_ $f(x) = x^2$ ist achsensymmetrisch zur y-Achse. + - **Punktsymmetrie zum Ursprung:** Wenn $f(-x) = -f(x)$ für alle $x \in D$. + - _Beispiel:_ $f(x) = x^3$ ist punktsymmetrisch zum Ursprung. + +4. **Nullstellen:** Bestimmung der x-Werte, für die $f(x) = 0$ gilt. + + - _Beispiel:_ $f(x) = x^2 - 4$. Nullstellen: $x^2 - 4 = 0 \Rightarrow x^2 = 4 \Rightarrow x_{1,2} = \pm 2$ + +5. **Schnittpunkte mit der y-Achse:** Berechnung von $f(0)$. + + - _Beispiel:_ $f(x) = x^2 - 4$. Schnittpunkt mit y-Achse: $f(0) = 0^2 - 4 = -4 \Rightarrow S_y(0, -4)$ + +6. **Verhalten im Unendlichen (Grenzwerte):** Untersuchung, was mit $f(x)$ passiert, wenn $x$ gegen $\infty$ oder $-\infty$ geht. + + - _Beispiel:_ $f(x) = \frac{1}{x}$. $\lim_{x \to \infty} \frac{1}{x} = 0$ und $\lim_{x \to -\infty} \frac{1}{x} = 0$ + +7. **Monotonie:** Bestimmung der Intervalle, in denen die Funktion steigt oder fällt. + + - **Monoton steigend:** Wenn $f'(x) > 0$. + - **Monoton fallend:** Wenn $f'(x) < 0$. + - _Beispiel:_ $f(x) = x^3$. $f'(x) = 3x^2 > 0$ für $x \neq 0$. Also ist $f(x)$ streng monoton steigend. + +8. **Extrempunkte (Hoch- und Tiefpunkte):** + + - **Notwendige Bedingung:** $f'(x) = 0$. + - **Hinreichende Bedingung:** + - **Hochpunkt:** $f'(x_0) = 0$ und $f''(x_0) < 0$. + - **Tiefpunkt:** $f'(x_0) = 0$ und $f''(x_0) > 0$. + - _Beispiel:_ $f(x) = x^2 - 4$. $f'(x) = 2x$. $f'(x) = 0 \Rightarrow x=0$. $f''(x) = 2 > 0$. Also hat $f(x)$ einen Tiefpunkt bei $T(0, -4)$. + +9. **Krümmungsverhalten:** + + - **Konvex (Linkskrümmung):** Wenn $f''(x) > 0$. + - **Konkav (Rechtskrümmung):** Wenn $f''(x) < 0$. + - _Beispiel:_ $f(x) = x^3$. $f''(x) = 6x$. Für $x>0$ ist $f(x)$ konvex, für $x<0$ ist $f(x)$ konkav. + +10. **Wendepunkte:** Punkte, an denen sich das Krümmungsverhalten ändert. + + - **Notwendige Bedingung:** $f''(x) = 0$. + - **Hinreichende Bedingung:** $f'''(x) \neq 0$. + - _Beispiel:_ $f(x) = x^3$. $f''(x) = 6x$. $f''(x) = 0 \Rightarrow x = 0$. $f'''(x) = 6 \neq 0$. Also hat $f(x)$ einen Wendepunkt bei $W(0, 0)$. + +11. **Skizze des Graphen:** Zeichnen des Funktionsgraphen basierend auf den gewonnenen Informationen. + +**Beispiel einer vollständigen Funktionsuntersuchung:** + +Untersuchen Sie die Funktion $f(x) = x^3 - 3x^2 + 2x$. + +1. **Definitionsmenge:** $D = \mathbb{R}$ (Polynomfunktion) +2. **Wertebereich:** $W = \mathbb{R}$ +3. **Symmetrie:** Keine offensichtliche Symmetrie. +4. **Nullstellen:** $x^3 - 3x^2 + 2x = 0 \Rightarrow x(x^2 - 3x + 2) = 0 \Rightarrow x(x-1)(x-2) = 0$. Nullstellen: $x_1 = 0, x_2 = 1, x_3 = 2$ +5. **Schnittpunkt mit y-Achse:** $f(0) = 0$. $S_y(0,0)$ +6. **Verhalten im Unendlichen:** $\lim_{x \to \infty} f(x) = \infty$, $\lim_{x \to -\infty} f(x) = -\infty$ +7. **Monotonie:** $f'(x) = 3x^2 - 6x + 2$. + - $f'(x) > 0$ für $x < 1 - \frac{1}{\sqrt{3}}$ und $x > 1 + \frac{1}{\sqrt{3}}$ (monoton steigend) + - $f'(x) < 0$ für $1 - \frac{1}{\sqrt{3}} < x < 1 + \frac{1}{\sqrt{3}}$ (monoton fallend) +8. **Extrempunkte:** $f'(x) = 3x^2 - 6x + 2 = 0$. + - Lösungen: $x_{1,2} = 1 \pm \frac{1}{\sqrt{3}}$. + - Hochpunkt bei ca. (0.42, 0.38) + - Tiefpunkt bei ca. (1.58, -0.38) +9. **Krümmungsverhalten:** $f''(x) = 6x - 6$. + - $f''(x) > 0$ für $x > 1$ (konvex) + - $f''(x) < 0$ für $x < 1$ (konkav) +10. **Wendepunkt:** $f''(x) = 6x - 6 = 0 \Rightarrow x = 1$. Wendepunkt $W(1, 0)$ +11. **Skizze:** (Hier würde eine Skizze des Graphen folgen, die die obigen Informationen berücksichtigt) diff --git a/shell.nix b/shell.nix index a58585b..babebf8 100644 --- a/shell.nix +++ b/shell.nix @@ -18,5 +18,7 @@ python312Packages.pandas python312Packages.jupyter python312Packages.ipykernel + + pre-commit ]; }

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[Stammbaumanalyse --- Wiederholung], + seminar: [Biologie Q2], + show-outline: true, + author: "Erik Grobecker", + date: datetime(day: 21, month: 11, year: 2024), + show-solutions: false, ) #show math.equation: set text(font: "New Computer Modern") //Wird für Mathe bei Grape-Suite gebraucht @@ -26,37 +26,44 @@ #let dom-geneal = add-persons( dom-geneal, ( - "I1": (sex: "m", phenos: ("ill",), geno-label: ("A", "a")), - "I2": (sex: "f", geno-label: ("a", "a")), + "I1": (sex: "m", phenos: ("ill",), geno-label: ("A", "a")), + "I2": (sex: "f", phenos: ("ill",), geno-label: ("A", "a")), "II1": (sex: "f", geno-label: ("a", "a")), - ) + ), +) +#let dom-geneal = add-unions( + dom-geneal, + (("I1", "I2"), ("II1",)), ) -// #let dom-geneal = add-unions( -// dom-geneal, -// (("I1", "I2"), ("II1",)) -// ) -Irgendein Test-Stammbaum: -// #canvas(length: 0.4cm, { -// draw-tree(dom-geneal) -// }) +Beweis eines dominanter Stammbaumes: +#canvas( + length: 0.4cm, + { + draw-tree(dom-geneal) + }, +) #let rez-geneal = genealogy-init() -#let rez-geneal = add-person( +#let rez-geneal = add-persons( rez-geneal, ( - "I1": (sex: "m"), - "I2": (sex: "f"), - "II1": (sex: "f", phenos: ("ill",)), - ) + "I1": (sex: "m", geno-label: ("A", "a")), + "I2": (sex: "f", geno-label: ("a", "a")), + "II1": (sex: "f", phenos: ("ill",), geno-label: ("a", "a")), + ), +) +#let rez-geneal = add-unions( + rez-geneal, + (("I1", "I2"), ("II1",)), +) +Beweis eines rezessiven Stammbaumes: +#canvas( + length: 0.4cm, + { + draw-tree(rez-geneal) + }, ) -// #let rez-geneal = add-unions( -// rez-geneal, -// (("I1", "I2"), ("II1",)) -// ) -// #canvas(length: 0.4cm, { -// draw-tree(rez-geneal) -// }) = Testen rezessiv -> siehe Kind 25 von 14 & 15\ @@ -71,6 +78,73 @@ liegt auf x-Chromosom -> ansonsten könnten nur Männer es haben => 4 & 5\ Da Tochter 22 nicht von der Krankheit welche ihre beiden Eltern, 16 und 17, plagt selber betroffen ist, kann diese nicht rezessiv sein, da wäre dies der Fall nur erkrankte Allele weitervererbt werden könnten, da rezessive Merkmale nur dann phänotypisch auftreten würden, sollten sie homozygotisch vorliegen. +#pagebreak() + = Hausaufgabe -mitochondrien werden nur von Müttern weitervererbt! +== M3 + +Nur Männer sind hier _Träger_, während Frauen nur _Überträger_ sind.\ +Da allerdings Frauen auch _übertragen_ ist es nicht y-Chromosomal. + +*Hinweise:* +- Krankheit tritt nur bei Männern vor -> gonosomal + +*Beweise:* +Anhand von 1, 2 und ihrem Kind 3 können wir sehen, dass es nicht *rezessiv* sein kann, da wenn dies der Fall wäre, zwei kranke Allele an 3 weitervererbt werden würden, da sowohl 1 als auch 2 die Krankheit tragen, 3 ist allerdings nicht krank was das Gegenteil beweist.\ +#h(1em) #sym.arrow.curve Hämophilie ist *dominant* + +== M4 --- Modellstammbaum einer seltenen mitochndrialen Vererbung + +#let m4-geneal = genealogy-init() +#let m4-geneal = add-persons( + m4-geneal, + ( + "I1": (sex: "f", phenos: ("ill",)), + "I2": (sex: "m"), + "II3": (sex: "m"), + "II4": (sex: "f", phenos: ("ill",)), + "II5": (sex: "f", phenos: ("ill",)), + "II6": (sex: "m"), + "II7": (sex: "f", phenos: ("ill",)), + "II8": (sex: "m", phenos: ("ill",)), + "II9": (sex: "m", phenos: ("ill",)), + "II10": (sex: "f"), + "III11": (sex: "f", phenos: ("ill",)), + "III12": (sex: "f", phenos: ("ill",)), + "III13": (sex: "f", phenos: ("ill",)), + "III14": (sex: "m", phenos: ("ill",)), + "III15": (sex: "m", phenos: ("ill",)), + "III16": (sex: "m"), + "III17": (sex: "f"), + "III18": (sex: "m"), + ), +) +#let m4-geneal = add-union( + m4-geneal, + ("I1", "I2"), + ("II4", "II5", "II7", "II8", "II9"), +) +#let m4-geneal = add-union( + m4-geneal, + ("II3", "II4"), + ("III11",), +) +#let m4-geneal = add-union( + m4-geneal, + ("II6", "II7"), + ("III12", "III13", "III14", "III15"), +) +#let m4-geneal = add-union( + m4-geneal, + ("II9", "II10"), + ("III16", "III17", "III18"), +) +#canvas( + length: 0.4cm, + { + draw-tree(m4-geneal) + }, +) +Wir können hier erkennen, dass wenn die Erkrankung bei einer Mutter auftritt, alle Kinder diese erhalten\ +#h(1em) -> Mitochondrien werden nur von Müttern weitervererbt! diff --git a/schule/geschichte/assets/Geschichte Q2 5.pdf b/schule/geschichte/assets/Geschichte Q2 5.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c92ef1e57af259634d43e258de33a6efd98dc202 GIT binary patch literal 492416 zcmeFacUV)~wmuvwqDYgDv>?(up@kL@q)M-fh!9YUfV3b|0wSRF-is(zM7pR*lisCC z6G3_j(n}yD-@>iuZtvOW{O-NazR&afzR&eX*2>CUbB;O2JI8p(m<#35RaOxY5rhzP zG|z9%ujX$*{n*?}ECv<^J6qWk%gTa*gP<)cNk=~p|LHIp&({1<&umzNo*eZQ2(V`(Udsj?Ibxpzhp06jA!++SWKRdv1}F#13j+ zWnf$2WhpcE%W1xN&mnrAR9*LN#-(RdqoG!OE#vbv9hldga0fO>(xydEXrrQM z7;Eq@8*{7fIhqZrmWCLv5-Yy=(zmsyL2GmD;}moy^|{5?W@=V)`ffV=d~GzPm+^IO z0fEJo`l*j*)(le&$<0>z^Z`2Srs0t_FtTkYt~3`jn4&KhkOfhXlc+JPkRCeQ*>O2o6PkGQ zQE$tj^3a>n;7y4+M*KIQ=3*hWx$F4_Dyd)ri1r8OSCO2LrE%AvkzD03P1$Lu$P`W1 zaVPiD$7k)?B#}(d=T=NhHUQgTqHS#la#eQ_8f=FT??g8p5jwmat&MGE-{Ga#8$tMI 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