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I know I know: studying the theory, experience and years of practise are essential. I know it, you know it.

However I am pretty sure there must be some particularly good resources (books, pdf books, pdf files, websites or what have you) or strategies (mathematica/matlab maybe? Stackexchange?) to improve "computationally".

By computationally I mean being quicker to evaluate things like integrals, ODEs, PDEs, integrals that you can solve with complex analysis etc. So, all those things that we all can do after a bachelor, but that allow people to sit on very different points of a scale. Some people are way way way better than others because they have practised more or had learned tricks. So my question is

What books, pdf files, websites, strategies, resources or tools (the most important would be books for me!!) can someone use to MASTER and PRACTISE (a lot, as in thousands per type if not more) the above computations (and related)?

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  • $\begingroup$ @Moo currently I am using MSE and Shaum's Outlines however I think they dont have enough exercises. Each book covers the whole syllabus of a 1 year course if not 2 and hence the exercises for , say, integrals are quite limited (I guess around 50 counting applications and triple/double integrals?). I don't know the others, is "Problem Solver Books" a title ? $\endgroup$ – Euler_Salter Dec 27 '16 at 0:07
  • $\begingroup$ @Moo I've got almost all Shaumans,but maybe you didn't understand my previous message. Yes surely 3000 exercises but on Calculus 1, 2 and 3. So there's barely 50 (maybe) on computational topics like the one stated above. Ive done all of those on integration and Im still average at it, I finished them in a day, thats not clearly enough to practise $\endgroup$ – Euler_Salter Dec 27 '16 at 0:44
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Some problem books are very useful for that. For instance, since you mentioned PDEs, I would suggest Claude Zuily's "Problems in distributions and partial differential equations" https://www.elsevier.com/books/problems-in-distributions-and-partial-differential-equations/zuily/978-0-444-70248-7.

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  • $\begingroup$ Thank you! Do you know any other good book for other topics? $\endgroup$ – Euler_Salter Dec 27 '16 at 1:28
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    $\begingroup$ For analytic number theory, there is Murty's "Problems in analytic number theory" springer.com/la/book/9780387723495. For more elementary stuff like integrals or ODEs, there are many books on these subjects, so you can just work out their exercises. In general, working out exercises (and also creating your own exercises!) is the best way to get computationally effective. $\endgroup$ – user316327 Dec 27 '16 at 10:34

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