Merge branch 'main' of gitea.mintcalc.com:alexander/TUM-Formelsammlungen

.gitea/workflows/build-script.yaml

@@ -51,3 +51,14 @@ jobs:
           name: typst-pdfs
           path: ${{ env.BUILD_DIR }}/*.pdf
           if-no-files-found: warn
+
+      - name: Create Gitea Release
+        uses: softprops/action-gh-release@v1
+        with:
+          tag_name: ${{ steps.tag.outputs.tag }}
+          name: Typst PDFs ${{ steps.tag.outputs.tag }}
+          body: |
+            Automated release of Typst-generated PDFs.
+
+            Commit: ${{ github.sha }}
+          files: ${{ env.BUILD_DIR }}/*.pdf

src/Analysis1.typ

@@ -202,8 +202,6 @@
 
       1. $e^x = sum_(n=0)^infinity (x^n)/(n!)$
       2. $ln(x) = sum_(n=0)^infinity (-1)^n x^(n+1)$
-      3. $sin(x) = sum_(n=0)^infinity $
-      4. $cos(x) = sum_(n=0)^infinity $
   ])
 )
 

src/Analysis_rewrite.typ

@@ -73,6 +73,42 @@
   ]
 
   #bgBlock(fill: colorAllgemein)[
+    #subHeading(fill: colorAllgemein)[Trigonometrie]
+  ]
+
+    #bgBlock(fill: colorAllgemein)[
+    #table(
+      inset: 1.5mm,
+      stroke: (thickness: 0.2mm),
+      columns: 4,
+      table.header(
+        [x], [deg], [cos(x)], [sin(x)]
+      ),
+      [$0$], [$0°$], [$1$], [$0$],
+      [$pi/6$], [$30°$], [$sqrt(3)/2$], [$1/2$],
+      [$pi/4$], [$45°$], [$sqrt(2)/2$], [$sqrt(2)/2$],
+      [$pi/3$], [$60°$], [$1/2$], [$sqrt(3)/2$],
+      [$pi/2$], [$90°$], [$0$], [$1$],
+      [$2/3pi$], [$120°$], [$-1/2$], [$sqrt(3)/2$],
+      [$3/4pi$], [$135°$], [$-sqrt(2)/2$], [$sqrt(2)/2$],
+      [$5/6pi$], [$150°$], [$-sqrt(3)/2$], [$1/2$],
+      [$pi$], [$180°$], [$-1$], [$0$],
+      [$3/2pi$], [$270°$], [$0$], [$-1$],
+      [$2pi$], [$360°$], [$1$], [$0$]
+    )
+  ]
+
+  #bgBlock(fill: colorAllgemein)[
+    #subHeading(fill: colorAllgemein)[Complexe Zahlen]
+    $z = r dot e^(phi i) = r (cos(phi) + i sin(phi))$
+
+    $z^n = r^n dot e^(phi i dot n) = r^n (cos(n phi) + i sin(n phi))$
+
+    #grid(
+      columns: (1fr, 1fr),
+      [$ sin(x) = (e^(i x) - e^(-i x))/(2i) $],
+      [$ cos(x) = (e^(i x) + e^(-i x))/(2) $]
+    )
     #subHeading(fill: colorAllgemein)[Trigonmetrie]
     $sin(x+y) = cos(x)sin(y) + sin(x)cos(y)$ \
     $cos(x+y) = cos(x)cos(y) - sin(x)sin(y)$ \
@@ -88,7 +124,7 @@
     )
 
     $cos^2(x) + sin^2(x) = 1$
-    
+    git config pull.rebase falsegit config pull.rebase false
     #grid(
       gutter: 5mm,
       columns: (auto, auto),
@@ -199,11 +235,16 @@
       row-gutter: 2mm,
       align: bottom,
       MathAlignLeft($ lim_(n->infinity) 1/n = 0 $),
-      MathAlignLeft($ lim_(n->infinity) q^n = 0 $),
-      MathAlignLeft($ lim_(n->infinity) q^n = 0 $),
-      grid.cell(colspan: 2, MathAlignLeft($ lim_(n->infinity) sqrt(n) = + infinity $)), [],
-      grid.cell(colspan: 2, MathAlignLeft($ lim_(n->infinity) k = k, k in RR $)), [],
-      grid.cell(colspan: 2, MathAlignLeft($ exp(x) =  e^x = lim_(n->infinity) (1 + x/n)^n $))
+      [],
+      MathAlignLeft($ lim_(n->infinity) k = k, k in RR $),
+      grid.cell(colspan: 2, MathAlignLeft($ exp(x) =  e^x = lim_(n->infinity) (1 + x/n)^n $)), 
+      MathAlignLeft($ lim_(n->infinity) sqrt(n) = + infinity $),
+      grid.cell(colspan: 2, MathAlignLeft($ lim_(n->infinity) q^n = cases(
+        0 &abs(q),
+        1 &q = 1,
+        plus.minus infinity &q < -1,
+        plus infinity #h(5mm) &q > 1
+      ) $)), []
     )
   ]
 
@@ -274,6 +315,20 @@
     #subHeading(fill: colorReihen)[Potenzreihen]
   ]
 
+  #bgBlock(fill: colorReihen)[
+    #subHeading(fill: colorReihen)[Bekannte Reihen]
+    *Geometrische Reihe:* $sum_(n=0)^infinity q^n$
+    - konvergent $abs(q) < 1$, divergent  $abs(q) >= 1$
+    - Grenzwert: (Muss $n=0$) $=1/(1-q)$
+
+    *Harmonische Reihe:* $sum_(n=0)^infinity 1/n = +infinity$
+    
+    *Andere*
+    - $e^x = limits(sum)_(n=0)^infinity (x^n)/(n!)$
+    - $ln(x) = limits(sum)_(n=0)^infinity (-1)^n x^(n+1)$
+  ]
+
+  #colbreak()
 
   #bgBlock(fill: colorAbleitung)[
     #subHeading(fill: colorAbleitung)[Funktionen]
@@ -414,3 +469,51 @@
 
   #colbreak()
 ]
+
+#pagebreak()
+
+== Folgen in $CC$
+
+$z_n in C: lim z_n  <=> lim abs(z_n -> infinity) = 0$
+
+Alle folgen regelen gelten
+
+Complexe Folge kann man in Realteil und Imag zerlegen
+
+z.B.
+
+$z_n = z^n z in CC$
+
+$z = abs(z) dot e^(i phi) = abs(z)^n$
+
+== Reihen in $CC$
+
+Fast alles gilt auch.
+
+Bis auf Leibnitzkriterium weil es keine Monotonie gibt
+
+Geometrische Reihe gilt.
+
+Exponential funktion
+
+#MathAlignLeft($ e^z = lim_(n -> infinity) (1 + z/n)^n = sum_(n=0)^infinity (z^n)/(n!) space z in CC $)
+
+Vorsicht: $(b^a)^n = b^(a dot c)$
+
+Potenzreihen: Eine Fn der form:
+
+#MathAlignLeft($ P(z) = sum^(infinity)_(n=0) a_n dot (z - z_0)^n space z, z_0 in CC $)
+
+=== Satz
+
+Konvergenz Radius $R = [0, infinity)$$$
+
+1. $R = 0$ Konvergiet nur bei $z = 0$
+
+2. $R in R : cases(
+  z in CC &abs(z - z_0) < R &: "abs Konvergent",
+  z in CC &abs(z - z_0) = R &: "keine Ahnung",
+  z in CC &abs(z - z_0) > R &: "Divergent"
+)$
+
+$ R = limsup_(n -> infinity) $