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I have a really hard time learning Double Integrals, which I attempted to understand when I first saw the use of polar co-ordinates for Integrals. So my goal is to learn double Integrals and also learn how polar co ordinates is being applied. I'm looking for a book that goes step by step, and which teaches me things like how $dx dy$ changes to $r dr d\theta$, (this is only one example) etc (everything).

In short I'm looking for something like "Double Integrals with polar co-ordinates for dummies"

Please help me. Thanks.

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    $\begingroup$ Basic multivariable calculus by Marsden, Tromba and Weinstein.. you can even look into Calculus -Vol2 by Tom M Apostol. Also Thomas Calculus may help $\endgroup$ – tattwamasi amrutam Dec 24 '14 at 12:17
  • $\begingroup$ @tattwamasiamrutam thank you so much, il check this out :) $\endgroup$ – M.S.E Dec 24 '14 at 12:17
  • $\begingroup$ What about advanced integration in several variables? I have yet to find a good book covering the more complicated techniques of double integration. $\endgroup$ – N3buchadnezzar Dec 24 '14 at 12:21
  • $\begingroup$ @N3buchadnezzar edit that to my question :) I would be glad to find a book that starts with easy things (which helps me) and goes upto advanced complicated stuff (solves problem for you) . $\endgroup$ – M.S.E Dec 24 '14 at 12:22
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    $\begingroup$ Have a look at Multivariable Calculus by James Stewart (chapter 15).... $\endgroup$ – Gggl. Dec 24 '14 at 12:47
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For double integration, I like the following two references:

  • Schaum's Outline of Advanced Calculus by Robert Wrede

http://www.amazon.co.uk/Schaums-Outline-Advanced-Calculus-Third/dp/0071623663/ref=sr_1_1?ie=UTF8&qid=1433163359&sr=8-1&keywords=schaum+outline+advanced+calculus

This has plenty of solved and unsolved problems and explains double integration well.

  • Multivariable Calculus by James Stewart

http://www.amazon.co.uk/Multivariable-Calculus-James-Stewart/dp/0538497874/ref=dp_ob_image_bk

Another great reference that I found breaks down double integration well.

Hope that helps.

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