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I. Differentiation – 6. Maksimum/minimum 126 6.23. 2. ordens kriterium ☞ [LA] 13.2 2.ordens partielle afledede, . . . Andenordenstest - Eksempel Funktionen f(x,y,z) = 2x 2 + 3y 2 − z 2 har gradient ∇(f) = (4x,6y, −2z) og kritisk punkt P = (0,0,0). Hesse matricen ⎛ 4 0 ⎞ 0 HP(f) = ⎝0 6 0 ⎠ har egenværdier 4,6 > 0 of −2 < 0. 0 0 −2 Andenordenstesten giver: P er et saddelpunkt. 6.24. Lokalt maksimum/minimum ☞ [S] 11.7 Maximum and minimum values To variabele - figur
I. Differentiation – 6. Maksimum/minimum 127 z har et saddelpunkt i (0,0). x z = 1 − x 2 + y 2 6.25. Ekstremumspunkters type ☞ [S] 11.7 Maximum and minimum values Eksempel 3 f(x,y) = x 4 + y 4 − 4xy + 1 har kritiske punkter, hvor De kritiske punkter bestemmes ∇f(x,y) = (4x 3 − 4y,4y 3 − 4x) = (0,0) x 3 − y = 0, y 3 − x = 0 ⇔ x 3 − y = 0, (x 3 ) 3 − x = 0 ⇔ y
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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 - 2. Partielle a
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II. Integration - 1. Dobbelt integr
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II. Integration - 2. Itereret integ
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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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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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IX. Opgaver - 5. Januar 2005 594 (t
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IX. Opgaver - 5. Januar 2005 600 Gr
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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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