limit of complex functions

[u04f061]

limits of complex functions

i've the book with name
advanced engineering mathematics
by
ervin kreyszig.
i am taking a course on complex analysis i.e complex functions,integration ,differention.
i want to study the limit theory of complex functions.
plz tell me how much it differs fromreal valued functions.
unfortunately the book i have has not much about this topic.
i want to study it deeply. if any one has helpful material about this plz help me.
if u have link to some other books plz give me

 

[LouisSheffield]

limit of complex function

I have a wonderful book that is (unfortunately) at home.
It even has intuitive examples.
I'll quote from it & pass the title & such on to you later.


The main "gist" of taking a limit of a complex function is quite similar to that of a real function, with the exception of the direction you approach the limit from.

For a real function, say f(x) = x, you can form the limit as you approach the value a
either from the left or from the right. If the function is analytic about a, the two limits are the same.

In complex functions, being analytic means that the limit is the same no matter how a is approached.
Imagine a small circle about a in the complex plane. Any point on the circle has a radius and an angle (amplitude and phase) relative to a.
As the radius shrinks to 0, we approach a.
If there is ANY dependence of the limit on the angle (or phase) that we approach from, the function is not analytic about the complex value a.

 

[u04f061]

limit of a complex function

i am thankful to u for this and i am deadly waiting for your new reply about the book and author.i want to inquire that have u studied the book i mentioned.would u prefer that book on the book u are prescribing?

 

[LouisSheffield]

limit complex function direction

Patient Friend -

Apologies for my having forgotten about this thread.

I don't believe I have the text you are using.
The one I have is Complex Analysis with Applications by Richard A. Silverman

I have 3 scanned page pairs to send to you.
In order to conserve storage in this forum, I have not attached them here.
I left a PM requesting an email address or an upload destination.

The scans cover the start of Complex Differentiation, where examples using complex limits best illustrate the points I had previously made.

The book is by Dover Publications - in the US, it is dirt-cheap as far as texts go.
**broken link removed**


Whatever text you end up using to supplement in your studies, make certain that it is intuitive to you in the sections that deal with complex integration.
With "complex integration", you'll find "complex" to be an understatement.


Again, kind regards for your patience ...

 

[haseebcu]

limits of complex integrals

kreyszig can help u alot