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So, I have reason to be returning to school, many years (5+) after my last attendance; and although I took (and passed, barely, after much strife) Calculus 1 and 2 at my previous university, I am very not secure in my knowledge of those topics.

What are some resources for me to self-review that material, outside of an academic framework? I have my old text-book, but I don't recall it being particularly accessible; and more importantly, I'd really like an accelerated approach that assumes prior knowledge of the material. (Books, websites welcome … I'm not a fan of video lecturing or similar, it seems a very slow way to consume information, but if you've a great resource, I suppose I'd take that too :P)

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    $\begingroup$ Khan academy is pretty good for early Calculus, even though it's pretty informal (and they're video lectures). Playing the videos at x1.25 speed makes it ok. Perhaps you want to expand what topics you need to review (I'm guessing sequences, integration, series, line integrals and such?). $\endgroup$
    – YoTengoUnLCD
    Jan 9, 2016 at 23:15
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    $\begingroup$ Presumably you're going to need some math for whatever you intend to do or this wouldn't come up. You say you just barely passed calculus five years ago. My advice is not to think about "reviewing" calculus, instead you should take the course again and learn it this time. Students who've just barely passed calculus are not ready for courses that depend on calculus, even if they took calculus the previous year. In your case it's going to be worse. Honest. Every time I teach differential equations I advise some students to retake calculus first. They never do. And they never pass DE. $\endgroup$
    – David C. Ullrich
    Jan 9, 2016 at 23:18
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    $\begingroup$ While not a great help to answer your question, I recommend laying out the learning objectives clearly. This will help you identify the breadth and depth you want to go to. $\endgroup$
    – NoChance
    Jan 9, 2016 at 23:19
  • $\begingroup$ It would be helpful if you could clarify certain points. How much do you know already? Do you value rigour? $\endgroup$
    – MathematicsStudent1122
    Jan 9, 2016 at 23:28
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    $\begingroup$ I would possibly suggest E-Z Calculus by Douglas Downing, although this doesn't answer your question exactly, because it's not for people who already know calculus. $\endgroup$
    – David
    Jan 10, 2016 at 2:04

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I would definitely check out Khan Academy. Although the website is based around video lecturing, the websites most effective feature are the exercises that are provided on every topic. You get immediate feedback on what you know and don't know. This can save you a lot of time. Then you only watch the lecture you need too. You can also speed the lectures up.

Here is a link to the website: https://www.khanacademy.org/math/algebra2

More importantly, If you had a difficult time at Calculus 5+ years ago, you maybe should start with Algebra II or similar, then work through Trigonometry, Precalculus, then Calculus. Although, this seems like a lot of work, by utilizing Khan Academy's practice exercise feature you may find that you remember the material and are able to spend less time on skills that you already know. This will allow you to identify skills that you are deficient in and allow you to study more effectively.

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  • $\begingroup$ A week in, I have to say: Khan Academy is exactly what I needed, despite having some video content. Great suggestion! $\endgroup$
    – ELLIOTTCABLE
    Jan 21, 2016 at 4:36
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I would say that for exercises, almost any calculus book should do. For reviewing fundamental concepts I think that Mathematics: From the Birth of Numbers by Jan Gullberg is a fairly good reference, just because it includes so many topics. If calculus was a struggle for you last time you went to school it might be good to review some of the pre-calculus material that is also included in this book. Also if you search this board I'm sure you will find many posts asking for the same advice, perhaps you will find what you are looking for among the answers to those questions.

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  • $\begingroup$ Check out e.g. William Chen's lecture notes $\endgroup$
    – vonbrand
    Jan 9, 2016 at 23:39

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