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Thread: Book Recommendation: Intergration methods

  1. #1 Book Recommendation: Intergration methods 
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    Hi, I'm new in this forum and I'd like to ask for any recommendation for books with intergrations methods. The troubling thing about intergrations is that there are many different ways of approaching an integral; which means that you may find your self struggling to solve an integral with trigonometrical substitutions when the solution only needs a simple application of the integration by paths method. In other words, its easy to mistake the idea of the solution. So what I'm looking for is books and material in general about integrals so that I can get an idea and put some methods in order.

    Thank you


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  3. #2 Re: Book Recommendation: Intergration methods 
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    Quote Originally Posted by panlotr
    Hi, I'm new in this forum and I'd like to ask for any recommendation for books with intergrations methods. The troubling thing about intergrations is that there are many different ways of approaching an integral; which means that you may find your self struggling to solve an integral with trigonometrical substitutions when the solution only needs a simple application of the integration by paths method. In other words, its easy to mistake the idea of the solution. So what I'm looking for is books and material in general about integrals so that I can get an idea and put some methods in order.

    Thank you
    Any calculus book will cover techniques of integration.

    Countour integral methods would be found in any text on complex analysis.

    After that it is just ingenuity, and a bit of luck in having an integral that is expressible in closed form.

    The most complete table is Gradshteyn and Ryzhik Table of Integrals, Series, and Products. http://www.mathtable.com/gr/


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    Thanks a lot for your reply, :wink:
    I've looked through many calculus books and they do cover techniques of intergration but the ones I've read are incomplete or focus only in a particular technique. Textbooks on complex analysis also include line integrals which I don't want to study yet. What I forgot to mention in my first post is that I'm also looking for exercises on integrals. As I've mentioned calculus books only have a small number of exercises for integrals since they usually comprise a small part of the book. This means that most of the time the thoughts they require for the solution are evident and included in the previous pages.

    Thanks again for your post and I'll check the book you recommended whenever I get the chance.
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  5. #4  
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    Quote Originally Posted by panlotr
    Thanks a lot for your reply, :wink:
    I've looked through many calculus books and they do cover techniques of intergration but the ones I've read are incomplete or focus only in a particular technique. Textbooks on complex analysis also include line integrals which I don't want to study yet. What I forgot to mention in my first post is that I'm also looking for exercises on integrals. As I've mentioned calculus books only have a small number of exercises for integrals since they usually comprise a small part of the book. This means that most of the time the thoughts they require for the solution are evident and included in the previous pages.

    Thanks again for your post and I'll check the book you recommended whenever I get the chance.
    I have no idea what you mean when you say calculus books ae incomplete. They are as complete as it gets as far as integration methods. There are simply not very many techniques. It is mostly a matter of ingenuity in the application of a limited number of tools.

    Mathematics is not really about evaluating nasty integrals. It is the concepts that are important. Evaluation of integrals is actually mundane. When I taught calculus I always found it to be the most boring topic in the course.

    It may surprise you to know that if you simply write down an integral it is quite likely to have no closed-form expression.

    If you just want a bunch of exercises, take your favorite table of integrals and derive the closed-form expression.
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    Yes I must admit it was an incorrect use of the the word incomplete, I may be misjudging the use of calculus books for my intention. It's just that I study physics and the curriculum of our subject "calculus" is indeterminate so I want to study a bit further.
    Thank you for your time
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  7. #6  
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    Quote Originally Posted by panlotr
    Yes I must admit it was an incorrect use of the the word incomplete, I may be misjudging the use of calculus books for my intention. It's just that I study physics and the curriculum of our subject "calculus" is indeterminate so I want to study a bit further.
    Thank you for your time
    To understand what calculus is really all about you would need to take a class or read a book on introductory real analysis. A couple of good ones are Elements of Real Analysis by Bartle and Principles of Mathematical Analysis by Rudin. You will see no emphasis on integration techniques, but you will see what really makes calculus work.

    In the sense of showing you the rigorous basis for calculus, elementary texts are indeed incomplete, but I don't think that is the sense that you meant. In terms of methods for evaluating integrals in closed form they do give you a fairly complete picture except for methods from complex analysis and integrals involving special functions.
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    Well our (meaning physics students) 2 math-related subjects of the first semester are calculus and linear algebra. I've understood a lot about calculus from high school, but the curriculum there didn't include sequences or any any material from real analysis. I'll try to find and study the books you've suggested to get an idea and hopefully to answer questions that I may have.

    Concerning integrations, I've had trouble finding the detailed solution of some integrals in calculus books. These integrals are:



    and



    What I don't understand is how the "h" gets into the solution..
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  9. #8  
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    Quote Originally Posted by panlotr
    Well our (meaning physics students) 2 math-related subjects of the first semester are calculus and linear algebra. I've understood a lot about calculus from high school, but the curriculum there didn't include sequences or any any material from real analysis. I'll try to find and study the books you've suggested to get an idea and hopefully to answer questions that I may have.

    Concerning integrations, I've had trouble finding the detailed solution of some integrals in calculus books. These integrals are:



    and



    What I don't understand is how the "h" gets into the solution..
    What h ?

    What are you talking about ?
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  10. #9  
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    ah sorry trouble with tex I suppose. The intergrals I mean are with "x" squared plus or minus "a" squared under the square root, for some reason the plus and the "a" were ommited so it seems like x in the 22th power..
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  11. #10  
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    Quote Originally Posted by panlotr
    ah sorry trouble with tex I suppose. The intergrals I mean are with "x" squared plus or minus "a" squared under the square root, for some reason the plus and the "a" were ommited so it seems like x in the 22th power..
    That I had figured out -- you missed a "space' in the tex. But what is h ?
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  12. #11  
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    Well if you look up the solution of the following integral in some calculus books, like THOMAS'S CALCULUS, you'll find that it equalls to:



    =

    (Sorry this is to complicated for TeX..) sin(h^(-1))(u/a) + C

    I know what sinh is but without the detailed solution I can't figure out how it ends up in the answer
    [/tex]
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  13. #12  
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    Quote Originally Posted by panlotr
    Well if you look up the solution of the following integral in some calculus books, like THOMAS'S CALCULUS, you'll find that it equalls to:



    =

    (Sorry this is to complicated for TeX..) sin(h^(-1))(u/a) + C

    I know what sinh is but without the detailed solution I can't figure out how it ends up in the answer
    [/tex]
    sinh is the hyperbolic sine. h is not a variable.
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