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Math Help - Good Book Covering Series Of Functions, Advance Analysis

  1. #1
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    Wink Good Book Covering Series Of Functions, Advance Analysis

    I need to find a good book covering these subjects:

    (Real) Series of functions (normal, simple, uniform convergence), complex series of functions (holomorphism, analyticity)

    Topology (open, closed, normes)

    And books covering a year or two after these subjects. I need books on analysis (advanced calculus) and not on other subjects.

    Just a note, I don't live in the US and do not attend an american university, so I can't just go to the nearest university bookstore. I need exact names of books so I can buy them online. I just find that american books are the most understandable.

    Thanks.
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  2. #2
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    Quote Originally Posted by PaulAtreides View Post
    I need to find a good book covering these subjects:

    (Real) Series of functions (normal, simple, uniform convergence), complex series of functions (holomorphism, analyticity)

    Topology (open, closed, normes)
    I have never seen a book that has both real and complex series covered in much detail at once. I would recommend a book that coveres real series extremely well, because complex series is basically the same thing. But then you ask to have topology in it as well, which makes it even more difficult.

    Have you ever heard of Amazon. You can search for anything you want there and it lets you preview some of books.
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  3. #3
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    Just a note, I don't live in the US .
    I assume then you live on Arrakis?.
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by galactus View Post
    I assume then you live on Arrakis?.
    Pffl. What book are you on? Arrakis was destroyed!

    -Dan
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  5. #5
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    Sorry for my ignorance. I am not that familiar with the entire series. Just the first one.
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    Smile Books

    Some of this you may find in Arfken & Weber Mathematical Methods for Physicists Academic Press ISBN 0-12-059816-7. This is an advanced undergraduate beginning grad student book. Has vectors, group rotations, series, good complex analysis plus standard physics fcns. Excellent! Great presentation of fundamental ideas in math and physics.

    Simpler books that give you good intuition on basic ideas are written by G F Simmons. He has one on (Ordinary) "Differential equations with applications and historical notes", 1972, and another one "Introduction to Topology and Modern analysis",1963, both McGraw-Hill. I read these myself in the 1970s. Don't know if they still sell.

    Also you can find brief excellent introductions to various subjects in the standard numerical book "Numerical recipes in C" by Press, Teukolsky, Vetterling and Flannery ISBN 0-521-43108-5 Cambridge University press (2nd ed) 1992. Buying this for 35 you also get computer code.

    MatLab is a computer software program that also provides you with a lot of knowledge and the ability to experiment with different functions.

    Unfortunately there are better books for students in Japanese and Chinese. I have a friend from Japan so I know although I cannot read it myself.
    Last edited by BasicIdeaIsSimple; July 18th 2007 at 06:15 PM. Reason: typo
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    Quote Originally Posted by BasicIdeaIsSimple View Post
    Some of this you may find in Arfken & Weber Mathematical Methods for Physicists Academic Press ISBN 0-12-059816-7. This is an advanced undergraduate beginning grad student book. Has vectors, group rotations, series, good complex analysis plus standard physics fcns. Excellent! Great presentation of fundamental ideas in math and physics.

    Simpler books that give you good intuition on basic ideas are written by G F Simmons. He has one on (Ordinary) "Differential equations with applications and historical notes", 1972, and another one "Introduction to Topology and Modern analysis",1963, both McGraw-Hill. I read these myself in the 1970s. Don't know if they still sell.

    Also you can find brief excellent introductions to various subjects in the standard numerical book "Numerical recipes in C" by Press, Teukolsky, Vetterling and Flannery ISBN 0-521-43108-5 Cambridge University press (2nd ed) 1992. Buying this for 35 you also get computer code.

    MathLab is a computer software program that also provides you with a lot of knowledge and the ability to experiment with different functions.

    Unfortunately there are better books for students in Japanese and Chinese. I have a friend from Japan so I know although I cannot read it myself.
    I would not recommend those books. The posters wants Mathematical books that have theory on Series. Those books have that material there but they do not present any theory.
    Except for "Introduction to Topology and Analysis" you mentioned.
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  8. #8
    Member kezman's Avatar
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    A good book I have is Mathematical Analisis of Tom Apostol, It has all of the topics you mentioned.(and more)
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  9. #9
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    Smile Yet another book

    Quote Originally Posted by ThePerfectHacker View Post
    I would not recommend those books. The posters wants Mathematical books that have theory on Series. Those books have that material there but they do not present any theory.
    Except for "Introduction to Topology and Analysis" you mentioned.
    Sorry, I agree about it not being too many series in those books. Also unclear about what level is desired. When I was an advanced undergraduate student in mathematics my professor recommended Rudin: Real and Complex Analysis, McGrawHill International Student Edition 1970, number 07 094189 0. This was taught to 1st year grad students in Wisconsin in the 1960s. Lots of power series and holomorphic functions. (I only studied part of it.)
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