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Please recommend a complex analysis book for The road to reality

  1. Feb 4, 2008 #1
    Please recommend a complex analysis book for "The road to reality"


    I am a electrical engineer who studied calculus III about 15 years ago. That time I memorized formulas to pass exams and never have much of a understanding of complex analysis. Never touched high math again after graduation.

    Here is my level:
    Calculus: Have some vague idea and memory on triple intergration fff.
    Complex analyisis: Have some vague memory on e^x = cosx + isinx.
    Complex fourier transform: Vague idea.
    My memory is lousy.

    Bought "The road to reality" by Roger Penrose with enthusiasm, ok until chapter 7 after many rereads. Then stuck at chapter 8 Riemann Surface. I don't understand the topological concepts.

    From this forum I read that there is a few books that can help:
    1. Visual Complex Analysis by Needham
    2. Complex variable by Flanigan
    3. Elementary theory of analytic functions of one and several complex variables by Henri Cartan

    I want a book that can help me understand intuitively the concepts in Penrose's book. I am not really interested in math proofs or graduate level detail math. Something like a book "for dummies", but not too shallow (hey, i am not that dumb).

    So which of the three math book you recommend to buy? Any other books? Thanks.
  2. jcsd
  3. Feb 4, 2008 #2
    Of the books you listed, I would recommend Visual Complex Analysis by Needham. It is a beautiful book, and also has the benefits of being relatively cheap and widely available (I've seen it on the shelves of Borders and Barnes & Noble many times).

    Amongst more traditional textbooks, my favorite is Fundamentals of Complex Analysis by Saff & Snider, but Complex Analysis by Stewart & Tall also seems to be widely used as an undergraduate textbook. I have also used Complex Variables and Applications by Brown & Churchill for a graduate-level course in applied complex analysis, but I am not a fan of that book.
  4. Feb 4, 2008 #3


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    Fundamentals of Complex Analysis by Saff & Snider

    is the only I have used, and it was quite ok. Many examples and exercises.
  5. Feb 5, 2008 #4
    I'd stay well away from "for dummies" if you're trying to understand the material. Most of those books shove easy-to-remember formulas down your throat. I like the suggestion of Visual Complex Analysis, but I'm of the opinion that (like differential geometry), you build intuition by getting your hands dirty. Somebody can tell you that analytic functions satisfy the maximum principle, but until you get into the trenches, you'll never understand why.
  6. Feb 13, 2008 #5
    Check These

    I suppose you don't know theory of complex variable well which is needed to understand the Riemann Surfaces in detail, i urge you to get book named Complex Analysis by Lars Ahlfors if you can, this is single most authentic reference by first field medalist and covers all the ideas pertaining to basics complex variable and some advanced things also. Besides a book on visual topology is also a must to appreciate the concept of Riemann Surfaces and the related transformation. Hope it would help, Regards K
  7. Aug 2, 2010 #6
    Re: Please recommend a complex analysis book for "The road to reality"

    I have got this book yesterday and have just come to know that complex analysis is required. i have books by Churchill, and Lars Alfors. Are these sufficient?
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