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