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Complex Analysis in Electrical Engineering

  1. Mar 26, 2012 #1
    Hi, Everyone!

    I just want to ask about the importance of Complex numbers analysis in the discipline of Electronics and Communications Engineering. I'm taking a course called, Analytical Methods in Engineering, and it's mostly focused on how to deal with complex numbers, from applying algebraic operations on them, to Cauchy–Riemann differential equations and so on.

    The problem is, the teacher of the course isn't capable of organizing himself to send the information clearly. Also, he teaches the course in a pure mathematics way, which means that he's not interested in providing calculations example, instead he rather to give proofs and verifications of established laws in the course. The result is, the course has become tedious and confusing for us, engineering students.

    I have yet to take any course related to communications, not even Electromagnetic waves, so here I come to ask, how much do I really need to know about complex analysis to be able to perform very good in communication courses, and to be able to design communication systems?

    Any recommended books on complex analysis for electrical engineers?

    Thanks
     
  2. jcsd
  3. Mar 26, 2012 #2

    rbj

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    even if this is presented in a dry mathematical manner, it will do you good, if you want to do well with communications and signal processing, to get most of the material in this course down hard. understanding stuff like contour integration, residue theory, etc will be useful to you in the future.
     
  4. Mar 26, 2012 #3
    Learn it. It will be useful.
     
  5. Mar 26, 2012 #4
    Basic knowledge is important for undergrad. It gets more important in post grad. Just complete the class and you'll be fine.
     
  6. Mar 26, 2012 #5
    Thanks for the answers. I would like you to recommend me best books explaining complex analysis from A to Z. I know that I can search for them, but I would like to take your expertise in this field.
     
  7. Mar 26, 2012 #6
    I used Introduction to Complex Variables and Applications [Hardcover] by Churchill.
     
  8. Mar 26, 2012 #7

    dlgoff

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    Me too. I'm looking at it right now. It's an awesome text. I can't believe my hardcover copy only cost $6 back when I was an undergrad.
     
  9. Mar 27, 2012 #8

    rbj

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    dig, you need to click off the Multi Quote button on posts you don't want included. it appears to work across threads. this has happened to me too.
     
  10. Mar 27, 2012 #9

    dlgoff

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    Multi Quote? I only see the Bob S quote that I intended. What are you seeing?

    Edit: Maybe you're thinking my signature quote came from multi-quoting?

    Edit2: BTW my initials are DLG not DIG. :mad:
     
    Last edited: Mar 27, 2012
  11. Mar 29, 2012 #10
    Well let me tell you two things.

    1) try to understand what is meant by a complex number : Its a combination of real and imaginary parts. Neither of the parts dominate each other in plane but on a whole, they dominate the value of the number. We, and almost every one, as accustomed to count from one to infinity along a straight line. (Maths is always one point of view which led to the birth of negative numbers i.e... reverse direction counting than turning back and counting, and vectors etc). Basically a number is an idea of something. Its a kind of adjective. Its based on its previous one. Like 3 is based on 2 and 2 based on 1. So, its like one point view. Assume yourself to be holding a ruler and counting along the ruler. Mathematics best describes this counting as having your eye at one end of the ruler and counting along the ruler with respect to a reference point. And, you will be successful in counting so with accurate results. Now, think, does it make any difference if I count the same number not along the ruler, but just a little above it? Its doesn't. (Assuming we are going in a line straight and parallel to our ruler). Well, that's what is an Imaginary number. The real part is our counting along the line, and our imaginary part is amount of lift above the scale. Haven't you ever wondered why only Imaginary scale is on Y-axis and real part on X-axis. This is the reason. As imaginary part doesn't alter you, there is no problem including it in your calculations. You might have seen that we never disturb or calculate an imaginary part with a real part. We never do it. Its the rule of Complex numbers.

    To introduce something of this sort, Mathematics took nearly thousand years ! What an amazing creation this one.. Now lets enter into the second one, its practical use.

    2) This is a bit complex but I am trying to make it short. We all know that a moving electron always produces magnetic field around itself. That neither effects the electron's motion nor the other electrons in its immediate neighborhood, in this analogical example. (Perhaps it affects, but its not yet proven or observed). This is best illustrated by Maxwell's experiments which involves something like placing two wires and currents going in opposite directions, then the wires attracting each other ; the currents in same direction they repell each other. Remember it?
    Now, neither of the two conductor's flow of charge is affected by this magnetic affect. But, there is an affect. (Its not yet proven that it effects precisely until the LHC's experiments succeed). Such affect is not perfectly affecting our quantity of concern (i.e... current), but is there. Now just apply this concept to the Complex number. Here the real part is the current in the conductors where as the imaginary part is the Magnetic force exhibited. As we have noted that counting parallel above or below doesn't matter, we are also including its imaginary part (magnetic flux). Now, as its not directly experienced, not atleast when our concern is current, we are taking into account but not allowing it into domination of our principal quantity. This is what complex numbers are always meant for.

    I think I explained it very less and very short. It takes a whole subject of a semester for me to analyze this. Its as simple here without vigorous explanations. But, it comes into more complex applications like, electromagnetic waves, where magnetic field dominates the electrical field and vice-versa, it takes hell out of us to calculate each of them at every point of time. Hope I conveyed you the basic answer for your question.

    Good luck and don't neglect it... Its a very important subject.. yes tedious but important. I just gave one single example, but there are many like transformers, antenna theory etc. . They are all based on this. Don't neglect it. I guess you get some idea about complex number after this and you should find it easy to read it if you understand what I said.
    Have a great day.. :)
     
  12. Mar 29, 2012 #11
    :rofl::rofl:
     
  13. Mar 30, 2012 #12
    Thank you everybody for you great contributions.

    As I said, the content of the course, and complex analysis in general, doesn't seem tedious to me, it's just the way my instructor presents it in an unorganized and confusing way, is what makes it tedious not just for me but for other classmates also. I don't hang my understanding of a subject on an instructor, so I have gathered a couple of references dedicated to explain complex analysis, and I'm ready to go.

    I hope I can gain as much knowledge as you guys currently have, if not much more.:smile:
     
  14. Mar 30, 2012 #13
    I'm going to have to order this once finals are over. Thanks!
     
  15. Mar 30, 2012 #14
    Learn it that way that he teaches, if u can learn it his way, u will sure be able to understand it when using in some practical examples in other courses ect.
     
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