Conference rusure::math

i think Prof. Knapp Books are a must for any complex variables study.
look at
  Knapp, Theory of functions.  Dover publishers.
  Knapp, Theory of functions , problem book 1,2
  in all i think Knapp has 4 books on theory of functions.

  i can list you more, but  a good way is to use your library computer
  and list all books that have call number QA 331.*  

  see also Kaplan , advanced calculas has good section on complex functions.
  also Kaplan , "into to analytic functions" 
  also Miller, "advanced complex analysis"  are good. 
  
  also Mackay "lectures on the theory of fucntions of complex variables"
  also Osgod, "topics in theory of functions of several complex variables"

 etc.. 

    oh, you also need the PROBLEM SOLVER book for COMPLEX ANALYSIS, it is 
    really good for exam practice, a lot of well solved problem. and if
    you are lucky like i were, you might find one or two of your homework
    problems in there !
    
/nasser
  
    

                     <<< Note 1493.0 by FROSTY::ESTRELLA >>>
                          -< complex analysis text?? >-

>>    I'm taking a complex analysis class.

>>    Could anyone point me to a complementary text?

The books by Knopp (not Knapp!) mentioned in .1 are classics; they present the
classical approach to complex analysis, and do it very well.

Another good classical-approach book is Titchmarch (sp?) Theory of functions.

For a non-standard approach, you may want to try the book by Cartan (theorie
des functions analytiques, if memory serves).  I believe it has been
translated into English, but for a math book that's no major deal (after all,
one *does* get used to the foreign equivalents of "thus", ..., rather quickly).
The book's most interesting feature is that it starts out with formal power
series and does everything from there.  It does require a certain degree of
mathematical maturity, though.

    the theory of functions series by Knorad KnOpp can be obtained from
    Dover books, it is a 5 volumn
    
    1. Elements of the theory of functions  #60154-4  $4.95
    2. Theory of functions, part 1.  #60156-0   $4.50
    3. Theory of functions, part 2.  #60157-9   $4.95
    4. problem book in the theory of functions vol 1   #60158-7  $4.95
    5.   "      "    "      "      "    "      vol 2   #60159-5  $4.95
    
    they dont take phone credit orders, send check to
    DOVER Publications, inc.  31 EAST 2nd St. Mineola, NY 11501
    add $2.50 postage and handling.
    their phone number is 516-294-7000 .
    
    /nasser

    The latest edition of Henri Cartan's _Theorie Elementaire des Fonctions
    Analytiques d'une ou Plusiers Variables Complexes_ is still in print,
    but the English translation which was available from Addison Wesley
    is long gone it seems.

    Serge Lang's text (from Springer) follows Cartan's approach and I think
    it is a very good elementary book, unlike some of Lang's others.

    In my opinion Ahlfors' book is a work of art and essential reading.

    A book I dislike is by Walter Rudin, _Real and Complex Analysis_.

    A wonderful two volume set that has lots of down to earth detail
    on all kinds of neat things is by Sansone and Gerretson - if you can
    locate this you'll know what I mean!  Volume I is on holomorphic
    functions and Vol II is on geometric theory, Riemann surfaces,
    automorphic functions... great stuff!  (anyone have copies they'll
    sell me? :-)

    Carrier, Krook and Pearson's application oriented book is still
    in print from Hod Books, Ithaca, NY.

    A book from Springer, by R. Remmert gives a historical viewpoint that
    you may find helpful.

    Finally, Henrici's three volume _Applied and Computational Complex
    Analysis_ is a goldmine of fascinating topics.  The first two are
    now in paperback.

    Chelsea has a number of classics reprinted, such as the ones by Hille,
    Caratheodory, Bieberbach; like Dover you can't beat the price.

    If you want references on Riemann surfaces I can say something about
    that.

    - Jim    

    Thanks for the info. Any others are also welcome.
    
    Dennis

    along these lines, the author named below lists (in his opinion) the 
    greatest "text" book .
    
    1. Introductio in analysin infiniorum by (who else) Euler.
       published in 2 volumns in 1748. author says only Latin, French
       and German editions are made of this work? no English edition
       of the greatest text book of all times?
    
    he also lists the Elements by Euclid , Al jabr of Al-Khowarizmi,
    Geometrie by Descartes, Principia by Newton and Disquisitiones by
    Gauss.
    
    but he claims these are not "really" text books, and the Introductio
    is #1 in his list.
    He outlines the reasons for his choice. 
    
    From American Mathematical Monthly, Vol 58 ( 1951) pp 223-226, author
    C.B.Boyer, Brooklyn College.
    
    Since this was written about 40 years ago, may be now an English
    translation exist for Introductio, now i remeber reading somewhere that
    all of Euler work is being collect into 75 volumns, and will be 
    published as the collected works of Euler, i dont know where i seem to
    have read this, and if that include translations too? 
    
    /nasser