- #1
Bacle
- 662
- 1
Hi, Everyone:
I was never clear n this point: given that z is a single complex variable,
how/why does it make sense to talk about z having partial derivatives.?
I mean, if we are given, say, f(x,y); R<sup>2</sup> -->R<sup>n</sup>
then it makes sense to talk about f<sub>x</sub> and f<sub>y</sub>, since
x and y are different variables. But , in f(z), z is a single variable, so there are no
additional variables to refer to, to meaningfully talk about partial derivatives.
Is it the case that a function of a complex variable z is also a function of two complex
variables.?. If not, is there a formal/theoretical argument to support this use.?
Thanks.
I was never clear n this point: given that z is a single complex variable,
how/why does it make sense to talk about z having partial derivatives.?
I mean, if we are given, say, f(x,y); R<sup>2</sup> -->R<sup>n</sup>
then it makes sense to talk about f<sub>x</sub> and f<sub>y</sub>, since
x and y are different variables. But , in f(z), z is a single variable, so there are no
additional variables to refer to, to meaningfully talk about partial derivatives.
Is it the case that a function of a complex variable z is also a function of two complex
variables.?. If not, is there a formal/theoretical argument to support this use.?
Thanks.