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I. Differentiation – 1. Kontinuitet 14 y Niveaukurver for f(x,y) = x 2 − y 2 y = √ x 2 4 1.9. Halvkugleskal ☞ [S] 11.1 Functions of several variables Eksempel 3,4,8 g(x,y) = 9 − x 2 − y 2 Grafen er en halvkugleskal Γg = {(x,y,z)|x 2 + y 2 ≤ 9,z = 9 − x 2 − y 2 } x
I. Differentiation – 1. Kontinuitet 15 Niveaukurver er cirkler = {(x,y,z)|x 2 + y 2 + z 2 = 9,z ≥ 0} g −1 (k) = {(x,y)|x 2 + y 2 ≤ 9, 9 − x 2 − y 2 = k} = {(x,y)|x 2 + y 2 = 9 − k 2 } 1.10. Globus ☞ [S] 11.1 Functions of several variables Figur z x Grafen for g(x,y) = 9 − x 2 − y 2 1.11. Breddegrader ☞ [S] 11.1 Functions of several variables y
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I. Differentiation - 4. Kædereglen
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II. Integration - 1. Dobbelt integr
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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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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 - 1. August 2002 540 y
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IX. Opgaver - 2. Januar 2003 552 z
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IX. Opgaver - 5. Januar 2005 594 (t
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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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