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III. Potensrækker – 3. Potensrækker 280 3. Potensrækker 3.1. Oversigt ☞ [S] 8.5, 8.6, 8.7, 8.10 Nøgleord og begreber ✌ Seks berømte potensrækker ✌ Potensrække ✌ Konvergensradius ✌ Differentiation og integration af potensrækker ✌ Taylor og MacLaurin rækker ✌ August 2002, opgave 4 ✌ Løsning af diff.-ligninger ved hjælp af rækker 3.2. Den geometriske række og eksponentialrækken ☞ [S] 8.7 Taylor ... Den geometriske række For alle tal x med |x| < 1 gælder Eksponentialrækken 1 1 − x = 1 + x + x2 + x 3 + ...
III. Potensrækker – 3. Potensrækker 281 For alle tal x ∈ R gælder e x = 1 + x x2 x3 + + + ... 1! 2! 3! 3.3. Cosinus og Sinus rækkerne ☞ [S] 8.7 Taylor and Maclaurin series Cosinusrækken For alle tal x ∈ R gælder Sinusrækken For alle tal x ∈ R gælder cos x = 1 − x2 2! sinx = x − x3 3! + x4 4! + x5 5! − ... − ... 3.4. Logaritme- og Arctan rækkerne ☞ [S] 8.7 Taylor and Maclaurin series Logaritmerækken For alle tal x med 0 < x ≤ 2 gælder Arctan rækken lnx = (x − 1) − (x − 1)2 2 + (x − 1)3 3 − ...
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CALCULUS "SLIDES" TIL CALCULUS 1 +
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3. Generelle områder 201 4. Koordi
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Forord "Slides" til forelæsningern
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I. Differentiation - 1. Kontinuitet
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II. Integration - 1. Dobbelt integr
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II. Integration - 4. Koordinatskift
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II. Integration - 4. Koordinatskift
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V. Matricer - 4. Determinanter 419
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V. Matricer - 4. Determinanter = (
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1. Egenvektorer VI Egenvektorer og
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Litteratur • Arnold, Ordinary dif
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0-række/søjle, 423 n-te afsnitssu
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Identitetsmatricen, 383 Identitetsm
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etningsafledede, 89, 102 retningsfe
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