Complex multivariate derivative
Suppose one is given
$f:mathbb{C}^2 rightarrow mathbb{C}^2$
$f(z_0, z_1) = (z_0z_1, 2z_0z_1)$
How would one find a total differential of such function?
My best guess is
$ df = (frac{partial(z_0z_1)}{partial{z_0}}, frac{partial(2z_0z_1)}{partial{z_0}})dz_0 + (frac{partial(2z_0z_1)}{partial{z_1}}, frac{partial(2z_0z_1)}{partial{z_1}})dz_1$
However, my understanding is limited and I'm not sure if it is correct. If somebody could confirm/deny that this is correct or provide more information, it would be great!
complex-analysis multivariable-calculus differential
asked Dec 12 '18 at 8:36
randrand
61
add a comment |
Suppose one is given
$f:mathbb{C}^2 rightarrow mathbb{C}^2$
$f(z_0, z_1) = (z_0z_1, 2z_0z_1)$
How would one find a total differential of such function?
My best guess is
$ df = (frac{partial(z_0z_1)}{partial{z_0}}, frac{partial(2z_0z_1)}{partial{z_0}})dz_0 + (frac{partial(2z_0z_1)}{partial{z_1}}, frac{partial(2z_0z_1)}{partial{z_1}})dz_1$
However, my understanding is limited and I'm not sure if it is correct. If somebody could confirm/deny that this is correct or provide more information, it would be great!
complex-analysis multivariable-calculus differential
asked Dec 12 '18 at 8:36
randrand
61
add a comment |
Suppose one is given
$f:mathbb{C}^2 rightarrow mathbb{C}^2$
$f(z_0, z_1) = (z_0z_1, 2z_0z_1)$
How would one find a total differential of such function?
My best guess is
$ df = (frac{partial(z_0z_1)}{partial{z_0}}, frac{partial(2z_0z_1)}{partial{z_0}})dz_0 + (frac{partial(2z_0z_1)}{partial{z_1}}, frac{partial(2z_0z_1)}{partial{z_1}})dz_1$
However, my understanding is limited and I'm not sure if it is correct. If somebody could confirm/deny that this is correct or provide more information, it would be great!
complex-analysis multivariable-calculus differential
asked Dec 12 '18 at 8:36
randrand
61
Suppose one is given
$f:mathbb{C}^2 rightarrow mathbb{C}^2$
$f(z_0, z_1) = (z_0z_1, 2z_0z_1)$
How would one find a total differential of such function?
My best guess is
$ df = (frac{partial(z_0z_1)}{partial{z_0}}, frac{partial(2z_0z_1)}{partial{z_0}})dz_0 + (frac{partial(2z_0z_1)}{partial{z_1}}, frac{partial(2z_0z_1)}{partial{z_1}})dz_1$
However, my understanding is limited and I'm not sure if it is correct. If somebody could confirm/deny that this is correct or provide more information, it would be great!
complex-analysis multivariable-calculus differential
complex-analysis multivariable-calculus differential
asked Dec 12 '18 at 8:36
randrand
61
asked Dec 12 '18 at 8:36
randrand
61
asked Dec 12 '18 at 8:36
randrand
61
asked Dec 12 '18 at 8:36
randrand
61
asked Dec 12 '18 at 8:36
randrand
61
61
add a comment |
add a comment |
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