This one wired trick
This commit is contained in:
54
src/Analysis1.typ
Normal file
54
src/Analysis1.typ
Normal 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
42
src/LinearAlgebra.typ
Normal 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
|
||||
]
|
||||
),
|
||||
|
||||
)
|
||||
0
src/Schaltungstheorie.typ
Normal file
0
src/Schaltungstheorie.typ
Normal file
23
src/lib/common.typ
Normal file
23
src/lib/common.typ
Normal 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
35
src/lib/styles.typ
Normal 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)
|
||||
*/
|
||||
Reference in New Issue
Block a user