Making Complex Numbers Interesting: Software & Books

In summary, the conversation discusses the difficulty and lack of interest in advanced topics in complex numbers, such as conformal mappings, residue theorem, series, and integrations. The speakers suggest various resources, such as Visual Complex Analysis by Needham and online visualization sites, to make these topics more understandable and enjoyable. The importance of conformal mappings in solving complex problems is also mentioned.
  • #1
rhia
37
0
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?
 
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  • #2
What, specifically, do you mean by the "advanced topics"?
 
  • #3
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.
 
  • #4
rhia said:
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.
 
  • #5
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
 
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  • #6
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).
 
  • #7
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.
 
  • #8
No, you dont' need computers, you need to read the books.
 
  • #9
rhia said:
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" :grumpy: edition.

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

http://www.oup.com/isbn/0-19-853446-9?view=in
 
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  • #10
The "low-priced" edition is still on a high side for me.
Thanks for helping!
 

What are complex numbers?

Complex numbers are numbers that consist of a real part and an imaginary part. The imaginary part is a multiple of the imaginary unit i, which is defined as the square root of -1. Complex numbers are written in the form a + bi, where a is the real part and bi is the imaginary part.

Why are complex numbers important?

Complex numbers are important in many fields of science and engineering, including mathematics, physics, and electrical engineering. They are used to represent and solve problems involving oscillations, waves, and electrical circuits.

What software can be used to work with complex numbers?

There are many software programs that can be used to work with complex numbers, including MATLAB, Mathematica, and Python. These programs have built-in functions for performing calculations with complex numbers and visualizing them in the complex plane.

Are there any books that can help me understand complex numbers?

Yes, there are many books available that can help you understand complex numbers, including "A First Course in Complex Analysis" by Matthias Beck and Gerald Marchesi, and "Complex Variables and Applications" by James Ward Brown and Ruel V. Churchill. These books cover the fundamentals of complex numbers and their applications in various fields.

How can complex numbers be made interesting?

Complex numbers can be made interesting by exploring their various properties and applications. This can include visualizing them in the complex plane, understanding their relationship to real-world phenomena, and solving challenging problems using complex numbers. Additionally, interactive software programs can make learning about complex numbers more engaging and hands-on.

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