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I. Differentiation – 4. Kædereglen 86 4.29. Opgave ☞ [S] 11.5 The chain rule Øvelse 19 x + y u = y + z x = p + r + t, y = p − r + t, z = p + r − t Beregn up. ux = 1 y + z −x + z uy = (y + z) 2 −x − y uz = (y + z) 2 4.30. Opgave ☞ [S] 11.5 The chain rule Øvelse 19 - fortsat x = p + r + t, y = p − r + t, z = p + r − t ux = 1 y + z , uy = −x + z (y + z) 2 , uz = −x − y (y + z) 2
I. Differentiation – 5. Gradient 87 5. Gradient up = up = uxxp + uyyp + uzzp y + z −x + z −x − y + + (y + z) 2 (y + z) 2 (y + z) 2 = −t p2 5.1. Oversigt ☞ [S] 11.6 Nøgleord og begreber ✌ Retningsafledt ✌ Gradientvektor ✌ Gradient i flere variable ✌ Fortolkning af gradientvektoren ✌ August 2002, opgave 5 5.2. Delvis afledt ☞ [S] 11.6 Directional derivatives and the . . . Definition - gentaget
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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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I. Differentiation - 6. Maksimum/mi
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I. Differentiation - 7. Lagrangemet
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II. Integration - 1. Dobbelt integr
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III. Potensrækker - 3. Potensrækk
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III. Potensrækker - 4. Taylorpolyn
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1. Grafiske/numeriske metoder IV Di
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IV. Differentialligninger - 1. Graf
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IV. Differentialligninger - 3. Gene
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1. Vektorer og matricer V Matricer
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V. Matricer - 1. Vektorer og matric
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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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VI. Egenvektorer og diagonalisering
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VIII. Appendiks - 1. Polære koordi
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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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