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IX. Opgaver – 1. August 2002 524 1.2. Oversigt ☞ Matematik Alfa 1, August 2002 Opgaver 1. Beregn et dobbeltintegral 2. Diagonaliser en 3 × 3−matrix 3. Bestem kritiske punkter og ekstrema 4. Angiv en potensrække og find en grænseværdi 5. Find gradient og retningsafledt 6. Beregn en ortogonal projektion 7. Løs en lineær differentialligning 1.3. Beregn et dobbeltintegral ☞ Matematik Alfa 1, August 2002 Opgave 1 Lad R betegne kvartcirkelskiven x2 + y2 ≤ 4, x ≥ 0,y ≥ 0. (Tegn.) Udregn R x2y dA. Løsning y 2 x
IX. Opgaver – 1. August 2002 525 R = {(x,y)|0 ≤ x,0 ≤ y,x 2 + y 2 ≤ 4} 1.4. Beregn et dobbeltintegral ☞ Matematik Alfa 1, August 2002 Opgave 1 - figur z x R = {(r,θ)|0 ≤ r ≤ 2,0 ≤ θ ≤ π 2 } 1.5. Beregn et dobbeltintegral ☞ Matematik Alfa 1, August 2002 y
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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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IX. Opgaver - 3. Januar 2004 574 L
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IX. Opgaver - 3. Januar 2004 580 Eg
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IX. Opgaver - 4. August 2004 582 =
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IX. Opgaver - 5. Januar 2005 592 De
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IX. Opgaver - 5. Januar 2005 594 (t
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IX. Opgaver - 5. Januar 2005 598 De
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IX. Opgaver - 5. Januar 2005 600 Gr
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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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