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S2/AnaMech/.unicourse
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S2/AnaMech/.unicourse
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name: Analytische Mechanik
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short: AnMe
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#import "./preamble.typ": *
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#show: conf.with(num: 4)
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#show: conf.with(num: 1)
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= Einleitung
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Newton < Lagrange < Hamilton
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#import "./preamble.typ": *
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#show: conf.with(num: 4)
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= Studienleistungen
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- mind. 2x vorrechnen
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= Integration
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#flashcard(0)[onw][
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sf
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]
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Idee:
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- Differenzieren:
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$
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F: I -> RR \
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F'(x) = lim_(x -> oo)
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$<okay>
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Die Idee ist nach einer Funktion zu fragen, welche die Vorschrift $F' = f$ erfuellt.
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Dazu kann in 2 Dimensionen der Flaecheninhalt unter dem Graphen der Funktion ermittelt werden.
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== Unbestimmte Integration
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Frage:
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Gegeben sei ein Intervall $I$ in RR und eine Funktion $f: I -> RR$
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Finden wir $F: I -> RR$ mit $F' = f$?
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#definition[
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Gegeben: $I <= RR$ Intervall
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$F, f: I -> RR$
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- $F$ eine Stammfunktion zu f auf I oder unbestimmtes
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]
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Beachte:
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Gegeben seien Stammfunktionen $F_1, F_2$ zu $f$
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$
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==> (F_1 - F_2)'(x) = f(x) - f(x) = 0\
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==> F_1 - F_2 "konstant auf" I
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$
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Man ueberprueft ob eine Funktion eine Stammfunktion ist anhand der Definition.
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Nicht jede Funktion hat eine Stammfunktion.
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#theorem[
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Zwischenwertsatz fuer Ableitungen
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Sei $F: [a,b] -> RR$ diffb.
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$
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==> F' "nimmt auf" (a,b) "jeden Wert zwischen" F'(a) "und" F'(b) "an".
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$ <zws>
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]
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#proof[
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// TODO: write this proof
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]
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Die Funktion, welche eine Stufenfunktion ist hat keine Stammfunktion, da sie im Widerspruch zu Satz @zws steht.
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#theorem[
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Summenregen fuer Integration
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Seien $I, I_0 "Intervalle in" RR$ uns $alpha_1, ... alpha_n in RR$
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- Gegeben:
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$f_1, ...,f_n I -> RR $
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// TODO: zuende schreiben
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]
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S2/AnaMech/template.typ
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S2/AnaMech/template.typ
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#import "./preamble.typ": *
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#show: conf.with(num: 1)
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= Uebersicht
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S2/CWR/.unicourse
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S2/CWR/.unicourse
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name: Computerwissenschaftliches Rechnen
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short: Cwr
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S2/CWR/pdfs/template.pdf
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S2/CWR/pdfs/template.pdf
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S2/CWR/template.typ
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S2/CWR/template.typ
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= Uebersicht
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S2/DiffII/.unicourse
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S2/DiffII/.unicourse
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name: Diff II
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short: DiII
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S2/DiffII/VL/DiIIVL2.typ
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S2/DiffII/VL/DiIIVL2.typ
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= Uebersicht bla
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S2/DiffII/VL/DiIIVL3.typ
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S2/DiffII/VL/DiIIVL3.typ
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#import "./preamble.typ": *
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#show: conf.with(num: 1)
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= Uebersicht
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S2/DiffII/VL/DiIIVL4.typ
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S2/DiffII/VL/DiIIVL4.typ
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// Diff template
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= Uebersicht
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S2/DiffII/pdfs/DiIIVL2.pdf
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S2/DiffII/pdfs/DiIIVL2.pdf
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S2/DiffII/pdfs/DiIIVL4.pdf
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S2/DiffII/pdfs/DiIIVL4.pdf
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S2/DiffII/template.typ
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S2/DiffII/template.typ
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// Diff template
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#import "./preamble.typ": *
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#show: conf.with(num: 1)
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= Uebersicht
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S2/ExPhyII/.unicourse
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S2/ExPhyII/.unicourse
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name: Experimentalphysik II
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short: ExII
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S2/ExPhyII/template.typ
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S2/ExPhyII/template.typ
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#import "./preamble.typ": *
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#show: conf.with(num: 1)
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= Uebersicht
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S2/Neuro/.unicourse
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S2/Neuro/.unicourse
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name: Computational Neuroscience
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short: Neuro
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S2/Neuro/NeuroVL1.typ
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S2/Neuro/NeuroVL1.typ
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S2/Neuro/VL/NeuroVL1.typ
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S2/Neuro/VL/NeuroVL1.typ
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#import "./preamble.typ": *
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#show: conf.with(num: 1)
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= Uebersicht
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S2/Neuro/template.typ
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S2/Neuro/template.typ
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#import "./preamble.typ": *
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#show: conf.with(num: 1)
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= Uebersicht
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= Einleitung
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Folien sind auf StudIP verfuegbar.
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# Links
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ExPhy Uebung Di 16-18 NR 7:
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https://ecampus.uni-goettingen.de/h1/pages/cs/sys/portal/hisinoneIframePage.faces?id=studip&navigationPosition=link_studip&url=https%3A%2F%2Fstudip-ecampus.uni-goettingen.de%2Findex.php%3Fsso%3Dcasgoe%26cancel_login%3D1%26again%3Dyes%26redirect_to%3Dhttps%253A%252F%252Fstudip-ecampus.uni-goettingen.de%252Fdispatch.php%252Fmy_courses%26redirect_token%3D947a61f0a9df959879bce689abac0ffa
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# Other modules
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Zusammenhang Mensch und Natur; Modul B.Phy.1609
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