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I've recently worked my way through high school math and am about to complete the linear algebra course (https://www.khanacademy.org/math/linear-algebra).

I've done most of the stuff on the precalculus playlist (not all on khan, some by books) - https://www.khanacademy.org/math/precalculus.

I struggle a bit finding the next playlist. It's obviously calculus, but there are a lot of playlist which seem to cover the same stuff:

There is "AP Calculus AB" and "BC" and I get that BC is AB + more stuff.

But there is as well "Differential Calculus" and "Integral Calculus" and "Differential Equations" and lots of other playlist and most of them have roughly but not exactly the same content.

What's the purpose of that and where do I continue?

Are there other online learning systems to recommend (I'm willing to pay and am not interested in a formal degree).

Edit: There is as well https://www.khanacademy.org/math/calculus-home, which looks like it covers everything.

shredding
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    The first four (not differential equations) should all have very large overlap; the first two are just focused on the specific curriculum of the US AP test, which is not really of specific interest for a self-learner, but they could still have good content. – Ian Aug 20 '17 at 18:56
  • Isn't differntial equations part of calculus (I'm from germany and am not yet fluent in the calculus vocabulary)? – shredding Aug 20 '17 at 19:00
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    In general, understanding integration requires knowing differentiation and both are required to understand differential equations, so there is a sort of natural order to the topics you mentioned. (And for both of them you should be somewhat fluent in limits) – mlk Aug 20 '17 at 19:01
  • Is it correct to say that calculus and differential equations are subtopics of analysis? – shredding Aug 20 '17 at 19:02
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    One could say that calculus is just the technique (Indeed, since you are from Germany, the translation is "Differential- und Integralrechnung", with emphasis on "Rechnung"). The theory behind both should be covered in a basic course on "Real analysis", however this is at university level. Differential equations are just a special kind of problem, however then again, the theory of differential equations definitely is a subtopic. – mlk Aug 20 '17 at 19:10
  • How much of the khan academy stuff is university level? The math e.g. in linear algebra is much more advanced (or into detail) then german highschool (gymnasium). – shredding Aug 20 '17 at 19:14
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    The level is hard to tell by just looking at the topics, however as an upper bound, I would say, that there is no topic in there, which would not be covered in the first year of university, even for an engineering degree. Although the university lecture of those topics would probably involve a lot more theory and details. As a lower bound, I had an ambitious teacher 10 years ago, back in school (also in Germany, although G9 instead of G8 as today), and I would say the only topic, we did not touch was differential equations. – mlk Aug 20 '17 at 19:34
  • I'm surprised you took linear before calc.. usually it's other way around – Ben G Jan 06 '22 at 02:50

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http://tutorial.math.lamar.edu

I highly recommend you to follow Paul's Math Notes, which contains everything from Algebra to Calculus III. His notes are highly readable, nicely organized, and filled with great examples.

For additional practice, I recommend Thomas' Calculus or Stewart Calculus.

kelvin
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