B14 Homeostasis at TU Braunschweig

Flashcards and summaries for B14 Homeostasis at the TU Braunschweig

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Was ist die Umgekehrte Dreiecksungleichung?

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Wie lautet die Couchy-Schwarz-Ungleichung?

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Was besagt die Dreiecksungleichung?
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Was besagt die umgekehrte Dreiecksungleichung?

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Cauchy-Schwarz-Ungleichung

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Definition von Konvergenz

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Rechenregeln für Grenzwerte
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Was ist asymptotische Gleichheit?

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Satz 3.9

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Einschließungsregel

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Satz 3.13
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Satz 5.11

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Exemplary flashcards for B14 Homeostasis at the TU Braunschweig on StudySmarter:

B14 Homeostasis

Was ist die Umgekehrte Dreiecksungleichung?
|x+y| ≥ ||x| - |y||

B14 Homeostasis

Wie lautet die Couchy-Schwarz-Ungleichung?
|| ≤ ||x|| * ||y||

B14 Homeostasis

Was besagt die Dreiecksungleichung?
|x+y| <= |x| + |y| mit Gleichheit genau für x, y mit gleichem Vorzeichen

B14 Homeostasis

Was besagt die umgekehrte Dreiecksungleichung?
|x+y| >= ||x| - |y|| mit Gleichheit genau für x, y mit verschiedenen Vorzeichen.

B14 Homeostasis

Cauchy-Schwarz-Ungleichung
|| <= ||x|| * ||y|| für Vektoren x, y mit Gleichheit genau dann, wenn x = y = 0 oder x = L*y für ein L in R.

B14 Homeostasis

Definition von Konvergenz
Eine komplexe Folge (an) konvergiert gegen a in C, falls für jede Genauigkeit e > 0 ein n0 in N existiert, sodass für alle n >= n0 gilt: |an - a| < e

B14 Homeostasis

Rechenregeln für Grenzwerte
- lim (an + bn) = a + b - lim (c * an) = c * a - lim (an * bn) = a * b - lim (an / bn) = a / b

B14 Homeostasis

Was ist asymptotische Gleichheit?
Zwei Folgen an und bn heißen asymptotisch gleich, falls lim (an / bn) = 1

B14 Homeostasis

Satz 3.9
Jede konvergente Folge an reeller Zahlen ist beschränkt.

B14 Homeostasis

Einschließungsregel
Es gelte an <= bn <= cn für alle bis auf endlich viele n. Falls d in R existiert mit lim (an) = d = lim (cn), dann gilt lim (bn) = d.

B14 Homeostasis

Satz 3.13
Für jede monoton wachsene/fallende Folge an gilt lim (an) = sup (an)/ inf (an).Insbesondere ist jeden beschränkte monotone Folge konvergent und jeden unbeschränkte monotone Folge uneigentlich konvergent.

B14 Homeostasis

Satz 5.11
Stetige Bilder kompakter Mengen sind kompakt.

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