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VIII. Appendiks – 1. Polære koordinater og komplekse tal 518 Den komplekse eksponentialfunktion er givet ved, z = x + yi, 7 e z = e x+yi = e x (cos y + isin y) Et specialtilfælde kaldes Eulers formel 6 e iy = cos y + isin y Eksponentialfunktionen opfylder den sædvanlige regneregel 5 e z1+z2 = e z1 e z2 1.31. Kompleks eksponentialfunktion ☞ [S] Appendix I Complex numbers Figur - eksponentialfunktion
VIII. Appendiks – 1. Polære koordinater og komplekse tal 519 Im 0 e x+yi 1.32. Kompleks eksponentialfunktion ☞ [S] Appendix I Complex numbers Eksempel 8 Beregn: (a) e iπ (b) e −1+iπ/2 Løsning e x y Re
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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 - 2. Januar 2003 568 De
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IX. Opgaver - 3. Januar 2004 572 2)
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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 594 (t
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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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