🚀 go-pugleaf

In article <T.Moore-240996120936@130.123.97.36>, T.Moore@massey.ac.nz
wrote:

In article <523t3u$i4a@newsbf02.news.aol.com>, tleko@aol.com (Tleko)
wrote:

>  I am not changing the variables x and y assigned to
>  the x,y plane. x and y are either positive or negative depending on the
>  quadrant in the plane where we analyze the analytic character of f(z).
>  In f(z)=x+iy  x and y are all positive and negative real numbers. 
>  We may write z=(+/-)x(+/-)iy without violating the CR conditions.

>     On this topic I will be glad to send you the volume VII referenced
in
>     the following paper:
> 
>  Subject: Complex Variables in  Engineering True or False?
> From: tleko@aol.com (Tleko)
> Date: 30 Jun 1996 12:58:14 -0400
> Message-ID: <4r6bn6$q87@newsbf02.news.aol.com>
> 
> From: Tleko@aol.com 
> 
>       Presented at the 1996 GAMM-Conference in Prague
>     
>       Leko, T.
>  
>       COMPLEX VARIABLES IN ENGINEERING TRUE OR FALSE?
>  
>       Abstract: This paper disproves the foremost
>       indispensible fundamental importance of Cauchy's
>       integrals in the theory of analytic functions of
>       a complex variable. In particular, Cauchy's
>       integral theorem, Cauchy's integral formula,
>       the definition of analyticity, Taylor's series
>       and Laurent's series have all escaped the
>       desired scrutiny.


>      YOUR COMMENTS WILL BE GREATLY APPRECIATED !

Now I understand what you are getting at, I see you are absolutely
correct. But only in your own system in which the derivative is
defined in a non-standard way. Whether your way is useful, I don't
know. But you will have to rederive all of complex analysis with
your new definition. Any theorem in which the real or imaginary
parts may change sign is at risk. For example, is Cauchy's
theorem true when the contour crosses quadrant boundaries?

I prefer the old complex analysis myself, but each to his/her own
taste.

Terry Moore, Statistics Department, Massey University, New Zealand.

Imagine a person with a gift of ridicule [He might say] First that a
negative quantity has no logarithm; secondly that a negative quantity has
no square root; thirdly that the first non-existent is to the second as
the
circumference of a circle is to the diameter. Augustus de Morgan

Thanks for quoting Augustus de Morgan.   Sincerely,  tleko@aol. com