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S2/CWR/VL/CwrVL6.typ

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+// Main VL template
+#import "../preamble.typ": *
+
+// Fix theorems to be shown the right way in this document
+#import "@preview/ctheorems:1.1.3": *
+#show: thmrules
+
+// Main settings call
+#show: conf.with(
+	// May add more flags here in the future
+	num: 5,
+	type: 0, // 0 normal, 1 exercise
+	date: datetime.today().display(),
+	//date: datetime(
+	//	year: 2025,
+	//	month: 5,
+	//	day: 1,
+	//).display(),
+)
+
+= Uebersicht
+
+= Partielle Differentialgleichungen
+
+ODE
+$
+	arrow(x) (t) => m (dif ^2 arrow(x)) / (dif t^2 )  =  F (arrow(x), dot(arrow(x))).
+$
+PDE
+$
+	(partial ^2 psi) / (partial t^2 ) =  u^2 (partial ^2 psi) / (partial x^2 ) , space psi (x,t) \
+	(partial T) / (partial t) =  D (partial ^2 T) / (partial x^2 ) , space "Fourier Gesetz" arrow(j) =  kappa arrow(nabla) T.
+$
+Poisson-Gleichung
+$
+	Delta phi =  - (rho (arrow(x))) / (epsilon_0 ).
+$
+Lineare partielle DGL
+$
+	L [phi (arrow(x))] =  rho (arrow(x)) \
+	phi (arrow(x)) =  phi_0 (arrow(x)) "auf Rand" partial Omega \
+	"gesucht ist die Loesung von Gebiet" Omega.
+$
+
+#example[
+	Poisson-Gleichung.
+
+	Fuehre eine Diffferenzdiskretisierung durch
+	$
+		phi (x,y) tilde.equiv phi (I_(x) , I_(y) ) \
+		Delta phi =  (partial ^2 phi) / (partial x^2 ) +  (partial ^2 phi) / (partial y^2 ) =  (phi (i_(x) + 1 , i_(y) ) - 2 phi (i_(x) , i_() )) / () 
+	$
+]
+
+Doolittle Verfahren
+Gauss-Elimination Verfahren
+