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IV. Differentialligninger – 3. Generelle metoder 350 For den logistiske ligning dP P = 0.08P(1 − dt 1000 ) prøver vi at tilnærme graferne for løsningerne med små tangentstykker. I et givet punkt (t1,P1) vil en tangent have ligning P = P1 + 0.08P1(1 − P1 )(t − t1) 1000 3.10. Grafisk løsning ☞ [S] 7.5 The logistic equation
IV. Differentialligninger – 3. Generelle metoder 351 Retningsfelt P 1000 0 100 3.11. Logistisk ligning - Eulers metode ☞ [S] 7.5 The logistic equation Eksempel 2 For det logistiske begyndelsesværdiproblem dP P = 0.08P(1 − ), P(0) = 100 dt 1000 prøver vi at tilnærme løsningen med differentialet i små intervaller. t
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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 - 4. Kædereglen
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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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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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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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