Start
Zufällige Seite
Anmelden
Einstellungen
Spenden
Über Wikiversity
Haftungsausschluss
Suchen
Hyperfläche/3 Variablen/Matrix zu Hauptteilen/Beispiel
Sprache
Beobachten
Bearbeiten
(
1
A
B
C
A
2
A
B
A
C
B
2
B
C
C
2
1
0
0
0
0
0
0
0
0
0
0
A
∂
∂
X
0
0
0
0
0
0
0
0
0
B
∂
∂
Y
0
0
0
0
0
0
0
0
0
C
∂
∂
Z
0
0
0
0
0
0
0
0
0
A
2
1
2
∂
2
∂
2
X
∂
∂
X
0
0
0
0
0
0
0
0
A
B
∂
2
∂
2
X
Y
∂
∂
Y
∂
∂
X
0
0
0
0
0
0
0
A
C
∂
2
∂
2
X
Z
∂
∂
Z
0
∂
∂
X
0
0
0
0
0
0
B
2
1
2
∂
2
∂
2
Y
0
∂
∂
Y
0
0
0
0
0
0
0
B
C
∂
2
∂
2
Y
Z
0
∂
∂
Z
∂
∂
Y
0
0
0
0
0
0
C
2
1
2
∂
2
∂
2
Z
0
0
∂
∂
Z
0
0
0
0
0
0
A
3
1
6
∂
3
∂
3
X
X
X
1
2
∂
2
∂
2
X
0
0
∂
∂
X
0
0
0
0
0
A
2
B
1
2
∂
3
∂
3
X
X
Y
∂
2
∂
2
X
Y
1
2
∂
2
∂
2
X
0
∂
∂
Y
∂
∂
X
0
0
0
0
A
2
C
∂
3
∂
3
X
X
Z
∂
2
∂
2
X
Z
0
1
2
∂
2
∂
2
X
∂
∂
Z
0
∂
∂
X
0
0
0
A
B
2
1
2
∂
3
∂
3
X
Y
Y
1
2
∂
2
∂
2
Y
∂
2
∂
2
X
Y
0
0
∂
∂
Y
0
∂
∂
X
0
0
A
B
C
∂
3
∂
3
X
Y
Z
∂
2
∂
2
Y
Z
∂
2
∂
2
X
Z
∂
2
∂
2
X
Y
0
∂
∂
Z
∂
∂
Y
0
∂
∂
X
0
A
C
2
1
2
∂
3
∂
3
X
Z
Z
1
2
∂
2
∂
2
Z
0
∂
2
∂
2
X
Z
0
0
∂
∂
Z
0
0
∂
∂
X
B
3
1
6
∂
3
∂
3
Y
Y
Y
0
1
2
∂
2
∂
2
Y
0
0
0
0
∂
∂
Y
0
0
B
2
C
1
2
∂
3
∂
3
Y
Y
Z
0
∂
2
∂
2
Y
Z
1
2
∂
2
∂
2
Y
0
0
0
∂
∂
Z
∂
∂
Y
0
B
C
2
1
2
∂
3
∂
3
Y
Z
Z
0
1
2
∂
2
∂
2
Z
∂
2
∂
2
Y
Z
0
0
0
0
∂
∂
Z
∂
∂
Y
C
3
1
6
∂
3
∂
3
Z
0
0
1
2
∂
2
∂
2
Z
0
0
0
0
0
∂
∂
Z
)
.
{\displaystyle {\begin{pmatrix}&1&A&B&C&A^{2}&AB&AC&B^{2}&BC&C^{2}\\1&0&0&0&0&0&0&0&0&0&0\\A&{\frac {\partial }{\partial X}}&0&0&0&0&0&0&0&0&0\\B&{\frac {\partial }{\partial Y}}&0&0&0&0&0&0&0&0&0\\C&{\frac {\partial }{\partial Z}}&0&0&0&0&0&0&0&0&0\\A^{2}&{\frac {1}{2}}{\frac {\partial ^{2}}{\partial ^{2}X}}&{\frac {\partial }{\partial X}}&0&0&0&0&0&0&0&0\\AB&{\frac {\partial ^{2}}{\partial ^{2}XY}}&{\frac {\partial }{\partial Y}}&{\frac {\partial }{\partial X}}&0&0&0&0&0&0&0\\AC&{\frac {\partial ^{2}}{\partial ^{2}XZ}}&{\frac {\partial }{\partial Z}}&0&{\frac {\partial }{\partial X}}&0&0&0&0&0&0\\B^{2}&{\frac {1}{2}}{\frac {\partial ^{2}}{\partial ^{2}Y}}&0&{\frac {\partial }{\partial Y}}&0&0&0&0&0&0&0\\BC&{\frac {\partial ^{2}}{\partial ^{2}YZ}}&0&{\frac {\partial }{\partial Z}}&{\frac {\partial }{\partial Y}}&0&0&0&0&0&0\\C^{2}&{\frac {1}{2}}{\frac {\partial ^{2}}{\partial ^{2}Z}}&0&0&{\frac {\partial }{\partial Z}}&0&0&0&0&0&0\\A^{3}&{\frac {1}{6}}{\frac {\partial ^{3}}{\partial ^{3}XXX}}&{\frac {1}{2}}{\frac {\partial ^{2}}{\partial ^{2}X}}&0&0&{\frac {\partial }{\partial X}}&0&0&0&0&0\\A^{2}B&{\frac {1}{2}}{\frac {\partial ^{3}}{\partial ^{3}XXY}}&{\frac {\partial ^{2}}{\partial ^{2}XY}}&{\frac {1}{2}}{\frac {\partial ^{2}}{\partial ^{2}X}}&0&{\frac {\partial }{\partial Y}}&{\frac {\partial }{\partial X}}&0&0&0&0\\A^{2}C&{\frac {\partial ^{3}}{\partial ^{3}XXZ}}&{\frac {\partial ^{2}}{\partial ^{2}XZ}}&0&{\frac {1}{2}}{\frac {\partial ^{2}}{\partial ^{2}X}}&{\frac {\partial }{\partial Z}}&0&{\frac {\partial }{\partial X}}&0&0&0\\AB^{2}&{\frac {1}{2}}{\frac {\partial ^{3}}{\partial ^{3}XYY}}&{\frac {1}{2}}{\frac {\partial ^{2}}{\partial ^{2}Y}}&{\frac {\partial ^{2}}{\partial ^{2}XY}}&0&0&{\frac {\partial }{\partial Y}}&0&{\frac {\partial }{\partial X}}&0&0\\ABC&{\frac {\partial ^{3}}{\partial ^{3}XYZ}}&{\frac {\partial ^{2}}{\partial ^{2}YZ}}&{\frac {\partial ^{2}}{\partial ^{2}XZ}}&{\frac {\partial ^{2}}{\partial ^{2}XY}}&0&{\frac {\partial }{\partial Z}}&{\frac {\partial }{\partial Y}}&0&{\frac {\partial }{\partial X}}&0\\AC^{2}&{\frac {1}{2}}{\frac {\partial ^{3}}{\partial ^{3}XZZ}}&{\frac {1}{2}}{\frac {\partial ^{2}}{\partial ^{2}Z}}&0&{\frac {\partial ^{2}}{\partial ^{2}XZ}}&0&0&{\frac {\partial }{\partial Z}}&0&0&{\frac {\partial }{\partial X}}\\B^{3}&{\frac {1}{6}}{\frac {\partial ^{3}}{\partial ^{3}YYY}}&0&{\frac {1}{2}}{\frac {\partial ^{2}}{\partial ^{2}Y}}&0&0&0&0&{\frac {\partial }{\partial Y}}&0&0\\B^{2}C&{\frac {1}{2}}{\frac {\partial ^{3}}{\partial ^{3}YYZ}}&0&{\frac {\partial ^{2}}{\partial ^{2}YZ}}&{\frac {1}{2}}{\frac {\partial ^{2}}{\partial ^{2}Y}}&0&0&0&{\frac {\partial }{\partial Z}}&{\frac {\partial }{\partial Y}}&0\\BC^{2}&{\frac {1}{2}}{\frac {\partial ^{3}}{\partial ^{3}YZZ}}&0&{\frac {1}{2}}{\frac {\partial ^{2}}{\partial ^{2}Z}}&{\frac {\partial ^{2}}{\partial ^{2}YZ}}&0&0&0&0&{\frac {\partial }{\partial Z}}&{\frac {\partial }{\partial Y}}\\C^{3}&{\frac {1}{6}}{\frac {\partial ^{3}}{\partial ^{3}Z}}&0&0&{\frac {1}{2}}{\frac {\partial ^{2}}{\partial ^{2}Z}}&0&0&0&0&0&{\frac {\partial }{\partial Z}}\end{pmatrix}}.}
