Making Complex Numbers Interesting: Software & Books

[rhia]

The advanced topics in complex nos are really boring and make no sense.
Is there any way I can make them interesting like any software or book which would make it easier and enjoyable?

 

[arildno]

What, specifically, do you mean by the "advanced topics"?

 

[rhia]

Topics like conformal mappings,residue theorem,series,integrations and the numerous results derived from them.I don't understand what use they are going to be of.

 

[hypermorphism]

Topics like conformal mappings,residue theorem,series,integrations and the numerous results derived from them.I don't understand what use they are going to be of.

If the ability to integrate seemingly unintegrable real integrands doesn't entice you, try Visual Complex Analysis by Needham for a more geometric approach.

 

[robphy]

As hypermorphism suggests, have a look at http://www.usfca.edu/vca/
which has a page of links http://www.usfca.edu/vca/websites.html

One of those listed sites is http://www.ima.umn.edu/~arnold/complex-g.html

For applications, look at the Complex Function Gallery of "Visual Quantum Mechanics"
http://www.kfunigraz.ac.at/imawww/vqm/gallery.html

 

[matt grime]

If you don't understand why conformal mappings are important then yo'ure missing something very very fundamental.

Suppose that we wish to model the velocity of a fluid traveling through a long pipe (ie "infinitely" long) with a simple set of boundary conditions. Easy, right? Now suppose that we wished to do it through a pipe that wasn't smooth, but had bumps, kinks, bends in it. The conformal mapping theorem allows us to translate a solution of the easy version to one for the hard one. (the equations governing the fow transform smoothly).

 

[rhia]

Thanks you all!After reading your replies I feel my approach to learning complex analysys was flawed.Can softwares like mathematica,mathcad,maple,matlab or others help me understand this course better?
Unfortunately Visual Complex Analysis by Needham isn't available in my country.

 

[matt grime]

No, you dont' need computers, you need to read the books.

 

[neutrino]

Unfortunately Visual Complex Analysis by Needham isn't available in my country.

I know atleast 3 places online where you can order the book from. Anyway, here are a couple of links for a "low-priced" edition.

http://firstandsecond.com/store/books/info/bookinfo.asp?txtSearch=1772106

http://www.oup.com/isbn/0-19-853446-9?view=in

 

[rhia]

The "low-priced" edition is still on a high side for me.
Thanks for helping!

 

[robphy]

Here's another visualization site "Complex Function Viewer"
http://www.math.ttu.edu/~pearce/complex/complexviewer.html