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IX. Opgaver – 1. August 2002 544 27 = 2 = 3√ 6 2 1.33. Beregn projektion ☞ Matematik Alfa 1, August 2002 Opgave 6 - figur v v u ∈ U ⊥ u = projU(v) Ortogonal projektion på underrum 1.34. Løs differentialligning ☞ Matematik Alfa 1, August 2002 Opgave 7 U
IX. Opgaver – 1. August 2002 545 Angiv den fuldstændige løsning til differentialligningen y ′ + 2y = xe −2x + 3 Angiv endvidere den partikulære løsning y(x), der opfylder y(0) = 2. Løsning a(x) = −2,b(x) = xe −2x + 3 1.35. Løs differentialligning ☞ Matematik Alfa 1, August 2002 Opgave 7 - løsning A(x) = a(x)dx = −2dx = −2x B(x) = e −A(x) b(x)dx = e 2x (xe −2x + 3)dx Som giver = 1 2 x2 + 3 2 e2x 1.36. Løs differentialligning ☞ Matematik Alfa 1, August 2002 Opgave 7 - løsning
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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 - 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 - 2. 1. o
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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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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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