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Need a good Analysis book

  1. Oct 31, 2010 #1
    Hello all,

    I study physics in English but at a German university. My current math class roughly follows the book "Königsberger Analysis 2" but I can't find a copy of this in English. I'm kind of in trouble because I don't learn very well from lectures, and only learn from going slowly through a text on my own. Last semester I just tried to revise my notes carefully after each lecture, but it didn't work out so well. So I would be grateful if somebody could recommend me an accessible, yet rigorous, analysis book that deals roughly with the topics of:

    Multivariable integral calculus (line integrals, volume integrals etc)
    Lebesque Integrals (measure theory)
    Complex Analysis
    Functional analysis (spaces and operators)

    Also, anything that has worked through examples, or questions with solutions is very much welcome.

  2. jcsd
  3. Oct 31, 2010 #2
  4. Oct 31, 2010 #3
    Cool, thanks for the link. I like the quote at the end by terrence tao:

    It's like if you want to be a good pianist,
    you have to do a lot of scales and a lot of practice,
    and a lot of that is kind of boring, it's work.
    But you need to do that before you can really be very expressive and really play beautiful music.
    You have to go through that phase of practice and drill.
    - Terry Tao

    I was just telling a friend how I decided recently to set aside a few hours a week, aside from homework, just for "practice" and review of the fundamentals
  5. Oct 31, 2010 #4


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    Mutivariable calculus: Burkill & burkill a second course in analysis.
    Lebeabue integrantion: Lebesgue Integration and measure by alan weir
    Comples analysis: complex analysis by priestly
    functional analysis: introductory functional analysis with applications, kreysig
  6. Oct 31, 2010 #5
    Thanks for the recomendations. I'll try and get my hands on them.
    Are they the books you used for your classes?
  7. Oct 31, 2010 #6


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    Homework Helper

    Yes. This was in 1993-1996
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