HN Academy

I took the (Penn) Calculus sequence by Robert Ghrist and really enjoyed it as a review of single variable calculus. He uses Taylor series as the basis of his explanations which I felt was really clean way to provide intuition for some of the more complicated theorems and formulae. The lecture videos have high quality animations and are broken into digestible chunks (around 10-15 minutes each). The downside is that only a few example problems are shown being worked out, but I only found this to be an issue for a few of the lectures (mainly in the applied calculus section of the course).

The course also covers some interesting, non-standard topics. In particular, I liked the lecture on a discrete version of calculus (https://www.youtube.com/watch?v=NHa8UgWigZk) which can be used to find easy solutions to series and recurrence relations (e.g. the "discrete anti-derivative" can be used to provide quick closed-form solutions to sums of the form "n^k from n=1 to K" - an example occurs at the 5:28 mark of the linked lecture, but some background from earlier in the video will be necessary to follow along).

The lecture videos are available on Youtube (https://www.youtube.com/playlist?list=PLKc2XOQp0dMwj9zAXD5Ll...), but I would recommend working through the problems on Coursera (especially the challenge problems) as well. I would also recommend that viewers watch the videos as 1.5x speed or faster. Dr. Ghrist speaks so slowly in these videos that I found it distracting.

For those who have some knowledge of the standard intro calculus textbooks, the level of rigor and difficulty in this course is above the Stewart book that many universities use, but below the Spivak/Apostol/Courant type of book that an honors course may use.

This used to be a single course, but Coursera split it up into 5 pieces, with somewhat unhelpful names. The sequence is "Part 1 - Functions"[1], "Part 2 - Differentiation"[2], "Part 3 - Integration"[3], "Part 4 - Applications"[4], and "Part 5 - Discrete Calculus"[5]. The first four parts names are reflected in their Coursera titles, but the "Discrete Calculus" course is titled "Single Variable Calculus" instead since it contains the final exam for the overall sequence.

It's also worth mentioning that Dr. Ghrist also has other video lectures available on Youtube (https://www.youtube.com/c/ProfGhristMath) for other math courses including a sequence on multivariable calculus called "Calculus Blue."

[1] https://www.coursera.org/learn/single-variable-calculus

[2] https://www.coursera.org/learn/differentiation-calculus

[3] https://www.coursera.org/learn/integration-calculus

[4] https://www.coursera.org/learn/applications-calculus

[5] https://www.coursera.org/learn/discrete-calculus