Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Which text? First course in complex analysis

  1. Jul 10, 2007 #1

    I am signing up to take my first course in complex analysis this upcoming semester at my university. One of the professors with whom I am interested in taking the class is using Complex Analysis 2nd edition by Bak & Newman and the other one is using Complex Variables & Applications 7th edition by Brown/Churchill. Can you comment on these books? Do you recommend one over the other? Why? If relevant, my preparation for the course includes a first course in real analysis using "baby Rudin" (that is, Rudin's Principles of Mathematical Analysis and not his more advanced text).

  2. jcsd
  3. Jul 10, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper

    churchill was the classic text for engineers for many years. it is a nice easy cookbook and one can learn from it. brown has revised it i guess.

    bak and newman sounds much more recnt and presumably modern but i do not know it.

    the analysts favorite is the somnewhat austere ahlfors, which actually ahs much to recommend it.

    my favorite is by henri cartan, but it helps to have some books with more problems and examples, and i like serge langs book quite well for both theory and problems.

    the amazing little book by knopp is too magical, as one somehow recalls nothing from reading its very succinct and clear explanations.

    it is crucial to get used to integration as path integration, and as something meASURING THE PRESENCE OF SINGULARITIES, NOT AREA.

    a terrific old fashioned book is the 2 volume set by,..... lets see who is that? oh yes, einar hille. and cartan and hille are available from dover i believe for a song.
    Last edited: Jul 10, 2007
  4. Jul 10, 2007 #3
    I happen to have the 7th edition of Brown and Churchill, and it has my recommendations. It's well written and clear, and it will have the information you need in it. From what I can gather of Bak and Newman (from Amazon's Search Inside), it's talky, and a bit more gentle.

    In addition to mathwonk's list of reccomendations, there's always Conway's Functions of One Complex Variable I, which is also a great choice. It goes at quite a slow pace, but it is thorough, and avoids using any fancy machinery to get things done.
  5. Jul 10, 2007 #4


    User Avatar
    Science Advisor
    Homework Helper

    except he uses sheaves for riemann surfaces which makes them look harder than necessary. since i love riemann surfaces, i am not partial to conway, but everyone else loves it.

    it does have some nice treatments of specific topics but i am not crazy about the overall organization.

    oh, and now ahlfors costs over 150 dollars. there is no book on complex variables worth over 50 bucks. cartan is a dover paperback for about $12.

    well conway is $48, brown/churchill is only $20, and oops, lang went up to $60. still 150 for ahlfors is a deal breaker.
    Last edited: Jul 10, 2007
  6. Jul 11, 2007 #5
    Thank you for the help. I've decided to take the course taught with Brown/Churchill. Which is good because the other class does fit my schedule.

    Hopefully I'll have the chance to take a second course in complex analysis (math isn't my primary major) and get the chance to cover more complex analysis in a more abstract respect.
  7. Aug 10, 2008 #6
    I used and like the Brown/Churchill text and continue to go back and refer to it.

    I used it in two courses, Complex I and II. I like to use it for science applics. and for seeing the comparison and uses of complex and real for solving heat, fluid, elctro probs.

    I used it with Dr. Zhou at Fayetteville State University in Fayetteville, NC.

    Please make some comments. I also posted a question on the comparison of complex and real techniques and have gotten no responses. Hope to get some response.

    Last edited: Aug 10, 2008
  8. Aug 13, 2008 #7


    User Avatar
    Science Advisor
    Homework Helper

    what are we supposed to comment on?
  9. Aug 13, 2008 #8
    Sir, First, I will upgrade. Second, I understand I will pay cash to upgrade?? Are international money orders accepted for this? Third, I have come across a number of students, others who have asked, pleaded for help and have expressed extreme frustration and have gotten nothing. Is this because they did not pay or is this the current low level of courtesy and lack of manners?

    I have taught and studied throughout the US at a variety of schools including Chapel Hill, NC State, and I want to know that I am not working with a bunch of snobs or rude academics. I want to recommend this sight and the people who could use it can pay.

    My question is: Is the Churchill/Brown the best text for the first course in Complex Analysis?

    Thanks for your consideration of my comments and for YOUR critique of the text.

    Although frustrated because of my own ignorance of because of what I have observed, I am really very interested in this Forum and would love to make use of it, whatever I need to pay. I just do not want to waste my time and money.

    Thanks for replying.

    Don Wire PhD

    Campbell University at Buies Creek, NC
  10. Oct 11, 2009 #9
    Alhfors is a pioneering text but lacks examples. Churchill is good but treatment of cauchy's theorem is incomplete. Conway is a mess as he starts with misleading def a function is analytic if it has continuous derivative and then shows continuity assunption is redundant. lang is good especially proofs are based on power series but wastes to much time in formal power series inverse function etc. again all these books except churchilluse homotopy notionforcauchy's thm which is unnecessary. homology is only necessary and really necessary for a satisfactory treatment. all the above books use unconstructive definition of pi based on mean value theorem.

    i have developed a complete yet simple treatment of cauchy's thm(devoid of homotopy) and also have an original constructive approach to elementary fuctions and angles.
  11. Oct 11, 2009 #10
    henry cartan is too advances but has a good treatmnment of both one and several variables. silvermann is good for aplications. knopp is good but dated.
  12. Jan 2, 2012 #11
    Having perused most of the texts offered above, I find that my favorite is Theory of Functions of a Complex Variable by A.I. Markushevich. I'm still learning the topic, but for me this one has been the clearest I've seen.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook