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IX. Opgaver – 5. Januar 2005 600 Gradienterne ∇f = (fx,fy) beregnes Så (0,0),(−1, −1) er kritiske punkter. 2) De andenordens partielle afledede er Hessematricen er I de kritiske punkter fås: ∇f(1,1) = (6,6) ∇f(0,0) = (0,0) ∇f(−1, −1) = (0,0) . fxx = 6x, fxy = 3, fyy = 6y . H(f) = H (0,0) (f) = 6x 3 3 6y 0 3 3 0 . , som har determinant = −9. Punktet (0,0) er derfor et saddelpunkt. −6 3 H (f) = , (−1,−1) 3 −6 som har karakteristisk polynomium −6 − λ 3 3 −6 − λ = λ2 + 12λ + 25
IX. Opgaver – 5. Januar 2005 601 med rødder −12±√ 144−100 2 < 0. Punktet (−1, −1) er derfor et lokalt maksimum, [LA] 13.2.
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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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I. Differentiation - 3. Tangentplan
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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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II. Integration - 2. Itereret integ
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II. Integration - 4. Koordinatskift
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III. Potensrækker - 1. l’Hospita
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III. Potensrækker - 2. Talfølger
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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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1. Vektorer og matricer V Matricer
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V. Matricer - 1. Vektorer og matric
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V. Matricer - 2. Lineære afbildnin
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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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IX. Opgaver - 1. August 2002 ⎡
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