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I. Differentiation – 5. Gradient 100 5.21. Gradient ☞ [S] 11.6 Directional derivatives and the . . . Eksempel - figur y (1,1) 1 u ∇f(1,1) ∇f(1,1) = (2,1), u = ( 3 4 5 , 5 ) 5.22. Retningsafledt ☞ [S] 11.6 Directional derivatives and the . . . Eksempel 4 Gradienten af f(x,y) = x 2 y 3 − 4y er ∇f(x,y) = (2xy 3 ,3x 2 y 2 − 4) For den retningsafledede i retning (2,5) bruges enhedsvektoren u = 1 √ 29 (2,5) x
I. Differentiation – 5. Gradient 101 Duf(x,y) = (2xy 3 ,3x 2 y 2 − 4) · 1 √ 29 (2,5) = 1 √ 29 (4xy 3 + 15x 2 y 2 − 20) 5.23. Retningsafledt ☞ [S] 11.6 Directional derivatives and the . . . Eksempel 4 - fortsat I retning u = 1 √ 29 (2,5) er I punktet (x,y) = (2, −1) fås Duf(x,y) = (2xy 3 ,3x 2 y 2 − 4) · Duf(2, −1) = (−4,8) · = 32 √ 29 1 √ 29 (2,5) 1 √ 29 (2,5) 5.24. Mange variable ☞ [S] 11.6 Directional derivatives and the . . . Bemærkning
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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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III. Potensrækker - 4. Taylorpolyn
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1. Grafiske/numeriske metoder IV Di
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1. Vektorer og matricer V Matricer
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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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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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