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I am re-studying functional analysis to prepare for my next year's PDE courses, I've taken it this year but I feel like I am not very good at it. May I ask what is the study routine/strategy for someone restudying it?

Usually, when I begin studying something as a beginner, I follow this routine: "intuition $\rightarrow$ exercise $\rightarrow$ see which topic I am not good at and focus". But I am not sure if that's the same procedure to follow as an intermediate learner.

I guess my question is both of the nature of "studying functional analysis" and "restudying a general topic or subject".

New:

Thanks for all your suggestions! By the way, I saw that Cambridge suggests Béla Bollobás' Linear Analysis, but I find it difficult to understand (a bit terse compared to the other books), am I stupid or what? If a book seems too hard should I switch, or press on try to understand?

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    $\begingroup$ What I do is writing a script with really detailed proofs to grasp every step and get a good understanding of the topics. Then I do exercises to test my knowledge and after every exercise I include them in my Script as examples or Corollaries. That takes a long time but is really fun imo. Other possibilities are just studying with books ig. $\endgroup$ Commented Jun 21, 2024 at 18:30
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    $\begingroup$ I'd go through a book that has exercises and solutions and just try to solve every exercise that is related to the topics you want to study. For PDEs, Alt - Linear Functional Analysis is quite nice, because it has solutions and focuses on applications. $\endgroup$ Commented Jun 21, 2024 at 18:52
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    $\begingroup$ I really liked Brezis book on functional analysis. There is a plethora of exercises and you can find the solutions online. $\endgroup$ Commented Jun 21, 2024 at 19:52
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    $\begingroup$ Yeap, that's it! $\endgroup$ Commented Jun 21, 2024 at 21:32
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    $\begingroup$ I would recommend finding something that suits your style. There is a plethora of books anyways $\endgroup$ Commented Jun 22, 2024 at 15:08

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