This one wired trick

This commit is contained in:
alexander
2025-11-10 23:35:28 +01:00
parent 5b1c954574
commit 23d4bda871
10 changed files with 3900 additions and 6 deletions

54
src/Analysis1.typ Normal file
View File

@@ -0,0 +1,54 @@
#import "@preview/biceps:0.0.1": *
#import "@preview/cetz:0.4.2"
#import "lib/styles.typ": *
#import "lib/common.typ": *
#show: stdTemplate
#flexwrap( // Trigonometric formulas
main-spacing: 1mm,
cross-spacing: 1mm,
stdBlock([
$sin(x+y) = cos(x)sin(y) + sin(x)cos(y)$ \
$cos(x+y) = cos(x)cos(y) - sin(x)sin(y)$ \
$cos(2x) = cos^2(x) - sin^2(x)$ \
$sin(2x) = 2sin(x)cos(x)$
#grid(
gutter: 5mm,
columns: (auto, auto),
[$cos^2(x) = (1 + cos(2x))/2$],
[$sin^2(x) = (1 - cos(2x))/2$]
)
$cos^2(x) + sin^2(x) = 1$
#grid(
gutter: 5mm,
columns: (auto, auto),
[$cos(-x) = cos(x)$],
[$sin(-x) = -sin(x)$],
)
Subsitution mit Hilfsvariable
#grid(
gutter: 5mm,
row-gutter: 3mm,
columns: (auto, auto),
[$tan(x)=sin(x)/cos(x)$],
[$cot(x)=cos(x)/sin(x)$],
[$tan(x)=-cot(x + pi/2)$],
[$cot(x)=-tan(x + pi/2)$],
[$cos(x - pi/2) = sin(x)$],
[$sin(x + pi/2) = cos(x)$],
)
$sin(x)cos(y) = 1/2sin(x - y) + 1/2sin(x + y)$
Für $x in [-1, 1]$ \
$arcsin(x) = -arccos(x) - pi/2 in [-pi/2, pi/2]$ \
$arccos(x) = -arcsin(x) + pi/2 in [0, pi]$
]),
sinTable
)

42
src/LinearAlgebra.typ Normal file
View File

@@ -0,0 +1,42 @@
#import "@preview/biceps:0.0.1" : *
#import "lib/styles.typ" : *
#show: stdTemplate
#flexwrap(
main-spacing: 1mm,
cross-spacing: 1mm,
stdBlock([
*Halbgruppe:* $(M, compose): M times M arrow M$
- Assoziativgesetz: $a dot (b dot c) = (a dot b) dot c$
*Monoid* Halbgruppe $M$ mit:
- Identitätselment: $e in M : a e = e a = a$
*Kommutativ/abelsch:* Halbgruppe/Monoid mit
- Kommutativgesetz; $a dot b = b dot a$
*Gruppe:* Monoid mit
- Inverse: $forall a in M : exists space a a^(-1) = a^(-1)a = e$
- Eindeutig Lösung für Gleichungen
- Auch kommutativ wenn: $a dot a = e$
*Ring:* Menge $M$ mit:
- Kommutativ Gruppe unter $(M, +)$,
- Halbgruppe unter $(M, dot)$
- Distributiv Gesetz: $(a + b) dot c = (a dot c) + (a dot b)$
*Körper:* Menge $M$ mit:
- Kommutativ Gruppe unter $(M, +)$
- Kommutativ Gruppe unter $(M, times)$
- Distributiv Gesetz: $(a + b) dot c = (a dot c) + (a dot b)$
]),
stdBlock(
[
*Injectiv:* one to one \
$f(x) = f(y) <=> x = y$
*Surjectiv:* Output space coverered \
- Zeigen das $f(f^(-1)(x)) = x$ für $x in DD$
Beweiß durch Wiederspruch \
für Gegenbeweiß
]
),
)

View File

23
src/lib/common.typ Normal file
View File

@@ -0,0 +1,23 @@
#import "styles.typ": *
#let sinTable = [
#table(
inset: 1.5mm,
stroke: (thickness: 0.2mm),
columns: 4,
table.header(
[x], [deg], [cos(x)], [sin(x)]
),
[$0$], [$0°$], hlMath([$1$], color: hlGreen), hlMath([$0$]),
[$pi/6$], [$30°$], hlMath([$sqrt(3)/2$], color: hlGreen), hlMath([$1/2$], color: hlGreen),
[$pi/4$], [$45°$], hlMath([$sqrt(2)/2$], color: hlGreen), hlMath([$sqrt(2)/2$], color: hlGreen),
[$pi/3$], [$60°$], hlMath([$1/2$], color: hlGreen), hlMath([$sqrt(3)/2$], color: hlGreen),
[$pi/2$], [$90°$], hlMath([$0$]), hlMath([$1$], color: hlGreen),
[$2/3pi$], [$120°$], hlMath([$-1/2$], color: hlRed), hlMath([$sqrt(3)/2$], color: hlGreen),
[$3/4pi$], [$135°$], hlMath([$-sqrt(2)/2$], color: hlRed), hlMath([$sqrt(2)/2$], color: hlGreen),
[$5/6pi$], [$150°$], hlMath([$-sqrt(3)/2$], color: hlRed), hlMath([$1/2$], color: hlGreen),
[$pi$], [$180°$], hlMath([$-1$], color: hlRed), hlMath([$0$]),
[$3/2pi$], [$270°$], hlMath([$0$]), hlMath([$-1$], color: hlRed),
[$2pi$], [$360°$], hlMath([$1$], color: hlGreen), hlMath([$0$] mm)
)
]

35
src/lib/styles.typ Normal file
View File

@@ -0,0 +1,35 @@
#let stdTemplate(doc) = [
#set text(
size: 8pt
)
#set page(
margin: 5mm
)
#doc
]
#let hlMath(content, color: rgb("#fffe69")) = box(
content,
outset: 2pt,
fill: color,
)
#let hlRed = rgb("#ff6969");
#let hlGreen = rgb("#76ff69");
#let stdBlock(content) = {
block(
stroke: 0.2mm,
spacing: 1mm,
inset: 2mm,
content
)
}
/* Usage examples:
#blockm("Hello", top: 10pt, bottom: 10pt)
#blockm(#p("Paragraph inside a margin-set block."), left: 12pt, right: 12pt)
*/