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https://texercises.com/exercise/parabolische-zylindrische-koordinaten/
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Exercise:
Gegeben sei die folge Koordinatentransformation in parabolische zylindrische Koordinaten: * x frac u^-v^ y uv z z * Berechne die Jacobi-Determinante für diese Transformation.

Solution:
* J_f pmatrix fracpartial xpartial u & fracpartial xpartial v & fracpartial xpartial z fracpartial ypartial u & fracpartial ypartial v & fracpartial ypartial z fracpartial zpartial u & fracpartial zpartial v & fracpartial zpartial z pmatrix pmatrix u & -v & v & u & & & pmatrix * Die Determinante dieser Matrix ist: det J_f u^+v^
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Exercise:
Gegeben sei die folge Koordinatentransformation in parabolische zylindrische Koordinaten: * x frac u^-v^ y uv z z * Berechne die Jacobi-Determinante für diese Transformation.

Solution:
* J_f pmatrix fracpartial xpartial u & fracpartial xpartial v & fracpartial xpartial z fracpartial ypartial u & fracpartial ypartial v & fracpartial ypartial z fracpartial zpartial u & fracpartial zpartial v & fracpartial zpartial z pmatrix pmatrix u & -v & v & u & & & pmatrix * Die Determinante dieser Matrix ist: det J_f u^+v^
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Tags
integralrechnung, jacobi-determinante, koordinatensystem, mechanik, physik
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Difficulty
(4, default)
Points
4 (default)
Language
GER (Deutsch)
Type
Calculative / Quantity
Creator uz
Decoration