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I. Differentiation – 1. Kontinuitet 12 Aktive væsker x,y,z blandes med proportional virkning Hvilket blandingsforhold giver størst virkning? V = xyz x + y + z = 1 V = xy(1 − x − y) D = {(x,y)|x > 0,y > 0,x + y < 1} Bestem maksimum for funktionen V på mængden D. 1.6. Graf og niveaukurve ☞ [S] 9.6, 11.1 Functions of several variables Definition Grafen for en funktion f : D → R er en flade i rummet R 3 . Γf = {(x,y,z)|(x,y) ∈ D,z = f(x,y)} Niveaukurven(konturlinjen) af kote k for en funktion f : D → R er en kurve i planen R 2 . Koter k vælges fra værdimængden. f −1 (k) = {(x,y) ∈ D|f(x,y) = k} 1.7. Udseende saddel ☞ [S] 11.1 Functions of several variables
I. Differentiation – 1. Kontinuitet 13 Figur x z Grafen af f(x,y) = x 2 − y 2 1.8. Udseende saddel ☞ [S] 11.1 Functions of several variables Figur y
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1. Grafiske/numeriske metoder IV Di
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V. Matricer - 4. Determinanter = (
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1. Egenvektorer VI Egenvektorer og
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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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