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I. Differentiation – 1. Kontinuitet 10 1.2. En generel funktion ☞ [S] 9.6 Functions and surfaces Figur y 0 D (x,y) x D ⊂ R 2 , f : D → R f(x,y) 1.3. Definitions- og værdimængde ☞ [S] 9.6 Functions and surfaces Definition En tilordning af et tal til et givet talpar definerer en funktion af to variable f : D → R
I. Differentiation – 1. Kontinuitet 11 Mængden af talpar kaldes definitionsmœngden. Mængden af tal kaldes vœrdimœngden. D ⊂ R 2 f(D) = {f(x,y) ∈ R |(x,y) ∈ D} 1.4. Bestem definitionsmængden ☞ [S] 11.1 Functions of several variables Eksempel 3 Forskriften g(x,y) = 9 − x 2 − y 2 giver en funktion med definitionsmængde D = {(x,y)|9 − x 2 − y 2 ≥ 0} = {(x,y)| x 2 + y 2 ≤ 3} som er cirkelskiven med centrum i 0 og radius 3. Værdimængden er intervallet g(D) = [0,3] ⊂ R 1.5. Et populært problem ☞ [S] 11.1 Functions of several variables Eksempel
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I. Differentiation - 3. Tangentplan
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I. Differentiation - 4. Kædereglen
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I. Differentiation - 5. Gradient 88
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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 - 3. Generelle omr
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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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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 - 2. Lineære afbildnin
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V. Matricer - 3. Lineære ligninger
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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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VII. Skalarprodukt og projektion -
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VIII. Appendiks - 1. Polære koordi
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IX. Opgaver - 1. August 2002 524 1.
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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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