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IV. Differentialligninger – 2. 1. ordens ligninger 334 2.19. Lineært system ☞ [LA] 15 Lineært system Notation 2 Givet 2 × 2-matricen A = (aij) og 2-søjlerne b = (bi), y(x) = (yi(x)) kaldes systemet dy = Ay dx homogent og er den homogene part af det inhomogene, b = 0, system dy = Ay + b dx 2.20. Superposition ☞ [LA] 15 Lineært system Sætning 26 Betragt 2 × 2-matricen A = (aij) og 2-søjlen y(x) = (yi(x)). Hvis z1(x),z2(x) er løsninger til det homogene lineœre differentialligningssystem så er enhver linearkombination også en løsning. dy = Ay dx z(x) = C1z1(x) + C2z2(x) 2.21. Superposition ☞ [LA] 15 Lineært system
IV. Differentialligninger – 2. 1. ordens ligninger 335 Sætning 26 - fortsat Betragt yderligere 2-søjlen b. Hvis z0(x) er en løsninger til det inhomogene lineœre differentialligningssystem dy = Ay + b dx så er enhver løsning af formen y(x) = z(x) + z0(x) hvor z(x) er en løsning til den homogene part af systemet. 2.22. Lineært system ☞ [LA] 15 Lineært system Eksempel 1 Systemet har diagonalmatricen som koefficientmatrix. e1,e2 er egenvektorer og basis for R 2 . y ′ 1 = λ1y1 y ′ 2 = λ2y2 λ1 0 Λ = 0 λ2 2.23. Lineært system ☞ [LA] 15 Lineært system Eksempel 1 - fortsat
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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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Litteratur • Arnold, Ordinary dif
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