Single-variable calculus learning recommendations

This page lists recommendations specific to learning single-variable calculus (called calculus for short here). This includes limits, differential calculus, integral calculus, and some auxiliary topics. This combines the calculus-related items in our online mathematics learning resources and the calculus-related items in our mathematics reading recommendations and sorts them based on your educational stage.

First-time learning

You're interested in self-studying calculus (roughly at the level of Advanced Placement BC calculus in the US), but with a deeper conceptual understanding and/or better problem-solving skills. The self-study could be undertaken prior to studying the subject at school, in parallel to school, or in place of studying the subject at school. The following are some high-quality resources that can offer you a relatively complete experience. We haven't made an attempt to be comprehensive here, but have listed the best sources.

If this description fits you ...	... this might be the best recommendation
You have an interest in solving challenging mathematical problems and discovering mathematical ideas through the problem-solving process.	The AoPS calculus text: Calculus by David Patrick, ISBN 978-1-934124-24-6, paperback. You can also enroll in the AoPS calculus class online, but this costs money, albeit an affordable sum of money.
You prefer to learn from videos that offer conceptual explanations of ideas, and you don't have an aversion to long videos.	The Center of Math calculus videos (here) and their corresponding textbook. These introduce ideas in a concepts-first fashion.
You like a nice integrated course experience with professionally done videos.	Calculus: Single Variable by Robert Ghrist (University of Pennsylvania) on Coursera, coursera.org/course/calcsing

Acquiring greater depth in calculus topics you already learned

You have already learned calculus at the Advanced Placement level or equivalent, but you feel that your understanding of the subject was inadequate. You want to acquire greater depth of understanding in some areas of the subject.

The first-time learner recommendations can be used for relearning. As a relearner, however, you have the advantage that you can also rely on resources that are very good for some important parts of the subject, even if they are not comprehensive and/or they are not uniformly good. Some such recommendations are:

• Vipul's Classroom has video playlists on some calculus-related topics, including limits, many subtopics of integration, differential equations, some subtopics of sequences and series.