Mixing
Is this a valid exercise?
$begingroup$
In Needham's Visual Complex analysis he sets the following exercise - Chapter 12 ex 12(i) on page 571:
Consider the image under an analytic mapping $f$ of a source of strength $S$ located at $p$.
(i) show geometrically, then algebraically, that if $p$ is not a critical point of $f$ (i.e., $f'(p)neq 0$) then the image is another source of strength $S$ at $f(p)$.
[A source of this type is given by $V=(S/2pi)(1/(overline{z}-overline{p})$]
I don't want a solution to the exercise because I want to try it myself, but I'm not convinced that it's a valid exercise because if $f$ is a general analytic function how can we be so specific about the image of the mapping?
complex-analysis
asked Jan 27 at 16:30
Ian TaylorIan Taylor
517
$endgroup$
add a comment |
$begingroup$
In Needham's Visual Complex analysis he sets the following exercise - Chapter 12 ex 12(i) on page 571:
Consider the image under an analytic mapping $f$ of a source of strength $S$ located at $p$.
(i) show geometrically, then algebraically, that if $p$ is not a critical point of $f$ (i.e., $f'(p)neq 0$) then the image is another source of strength $S$ at $f(p)$.
[A source of this type is given by $V=(S/2pi)(1/(overline{z}-overline{p})$]
I don't want a solution to the exercise because I want to try it myself, but I'm not convinced that it's a valid exercise because if $f$ is a general analytic function how can we be so specific about the image of the mapping?
complex-analysis
asked Jan 27 at 16:30
Ian TaylorIan Taylor
517
$endgroup$
add a comment |
$begingroup$
In Needham's Visual Complex analysis he sets the following exercise - Chapter 12 ex 12(i) on page 571:
Consider the image under an analytic mapping $f$ of a source of strength $S$ located at $p$.
(i) show geometrically, then algebraically, that if $p$ is not a critical point of $f$ (i.e., $f'(p)neq 0$) then the image is another source of strength $S$ at $f(p)$.
[A source of this type is given by $V=(S/2pi)(1/(overline{z}-overline{p})$]
I don't want a solution to the exercise because I want to try it myself, but I'm not convinced that it's a valid exercise because if $f$ is a general analytic function how can we be so specific about the image of the mapping?
complex-analysis
asked Jan 27 at 16:30
Ian TaylorIan Taylor
517
$endgroup$
In Needham's Visual Complex analysis he sets the following exercise - Chapter 12 ex 12(i) on page 571:
Consider the image under an analytic mapping $f$ of a source of strength $S$ located at $p$.
(i) show geometrically, then algebraically, that if $p$ is not a critical point of $f$ (i.e., $f'(p)neq 0$) then the image is another source of strength $S$ at $f(p)$.
[A source of this type is given by $V=(S/2pi)(1/(overline{z}-overline{p})$]
I don't want a solution to the exercise because I want to try it myself, but I'm not convinced that it's a valid exercise because if $f$ is a general analytic function how can we be so specific about the image of the mapping?
complex-analysis
complex-analysis
asked Jan 27 at 16:30
Ian TaylorIan Taylor
517
asked Jan 27 at 16:30
Ian TaylorIan Taylor
517
edited Jan 27 at 19:20
Ian Taylor
asked Jan 27 at 16:30
Ian TaylorIan Taylor
517
asked Jan 27 at 16:30
Ian TaylorIan Taylor
517
asked Jan 27 at 16:30
Ian TaylorIan Taylor
517
517
add a comment |
add a comment |
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