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omyojj
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partial derivative with respect to z & z_bar??
Hi, all..
While I`m reading the Ahlfors` complex analysis..I`ve found a tricky expressions about partial derivatives..
On the theory of analytic fns.
author uses the expressions ∂f/∂z , ∂f/∂z_bar (z_bar - complex conjugate)
with f=f(x,y)(f is a complex fn of two real variables..)
by introducing z=x+iy, z_bar=x-iy as new "independent" variables..
By the way, can z and z_bar be independent? Moreover, if we write f(z,z_bar) instead,
the expression ∂f(z,z_bar)/∂z seems to be misleading in a sense that the conventional
definition of partial derivative tells us that z_bar must be fixed while z varies ( which cannot be)
Can anybody give me an answer for this?
Hi, all..
While I`m reading the Ahlfors` complex analysis..I`ve found a tricky expressions about partial derivatives..
On the theory of analytic fns.
author uses the expressions ∂f/∂z , ∂f/∂z_bar (z_bar - complex conjugate)
with f=f(x,y)(f is a complex fn of two real variables..)
by introducing z=x+iy, z_bar=x-iy as new "independent" variables..
By the way, can z and z_bar be independent? Moreover, if we write f(z,z_bar) instead,
the expression ∂f(z,z_bar)/∂z seems to be misleading in a sense that the conventional
definition of partial derivative tells us that z_bar must be fixed while z varies ( which cannot be)
Can anybody give me an answer for this?
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