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I am currently studying Calculus and there are some topics giving me some difficulty, such as the epsilon-delta definition of a limit. I searched the Internet and found that this epsilon-delta definition is not particularly important in Calculus study, but more so in Analysis, and since my focus is primarily in Calculus, I could skip it.

My question is what other topics in Calculus books (differential and integral) could I skip?

Edit: 1/7/15

I kept searching and found this question and answer on Mathematics Stack Exchange that talks about what topics could be studied in Real analysis, Complex analysis, and differential equations. These topics are ordered which is helpful.

My new request is for suggestions based on the links provided. I am unable to contact the writer of the posted answer. If you could also provide What books would be helpful for any suggestions, it would be greatly appreciated.

Please keep in mind that I am a beginner and I'm looking for something that provides gradual increases in difficulty.

Thanks in advance.

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    $\begingroup$ That depends. What do you plan to do in the future that would use calculus? Which further math classes do you plan to take? $\endgroup$ – Rory Daulton Nov 30 '14 at 23:54
  • $\begingroup$ If you are intending on using it in real life, then learn programming and numerical calculus methods. In real life hardly anything is simple enough to be solved analytically. If you are wanting to learn enough to skip Calc 101, do everything. If you are doing it for fun, learn whatever catches your interest, but don't spend too long on Calculus before you do linear algebra, discrete maths, and many other genuinely useful and fascinating areas of maths. $\endgroup$ – Richard Jan 1 '15 at 11:02
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I think it's important to keep in mind that reading a mathematics textbook is not the same as reading other texts. I direct you to the MESE answer that discusses this at length here, which may help you to determine what topics to skip.

In general, there is value in going over every topic in a textbook, but I doubt many people completely understand every single topic to their fullest degree the first time meeting a new field. Constant reviewing and rereading of material is the best way to make gains in comprehension.

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I wouldn't recommend skipping anything. If you've found a calculus book with good reviews, it's likely that it's set up in such a way that it provides an organic progression between topics.

I somewhat disagree that the epsilon delta definition of limits should be skipped while learning calculus. While it's not immediately useful in solving limits (since there are other techniques), it does provide valuable insight into how we go about dealing with infinitesimal change.

This ends up providing you with some useful intuition when progressing further into differential/integral calculus.

So my bottom line is; learn limits the "simplified" way first. Then learn epsilon delta. Learning the simplified way first might help you digest the latter more easily.

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