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This superb course is delightfully brain-rackingly difficult in all the best senses of the word. The presentation of the material is outstanding. Professor Ghrist "speaks math", that is, conveys complex mathematical notions in mere words in a manner more fastidiously clear than anyone I've ever heard. In addition, he provides an original and entertaining visual presentation of the material for more impact. There is a concise calculus wiki which basically functions as a helpful textbook companion. But getting to the part about difficult... First off, the range of material is vast. In addition to the more standard material on differentiation and integration, Taylor series, BigO, discrete calculus and extensive applications of calculus are covered. There is bonus material for the more advanced as well as bonus homework for those up to the task. Fortunately, it is only necessary to learn the "core" material to pass the course. The homework is not graded but for each quiz one has only a single submission. One gets credit the first attempt or not at all. After about 14 weeks, one takes a final exam worth 80% of the grade. Again, there is one shot to get it right. All tests are to be taken without notes, calculators, Wolfram-Alpha or any other support. I guesstimate that the attrition rate of the class was around 80% (only 20% finished) and that the pass rate was around 10% of those who started. The official figures were not released. I do not recommend this class for those with little prior exposure to calculus. I highly recommend it to those with the motivation, time and fortitude to learn a whole lot of math at the feet of one of the true masters of the craft.

Excellent review of mechanics. As others have said, the course assumes prior exposure to mechanics and I would not recommend it as an introduction. That said, it is a relatively thorough review of basic mechanics. It concentrates largely on the concepts and less so on the math. A good command of algebra and trigonometry is needed, but only basic calculus (some derivation and some integration) is used. Vector analysis likewise is only touched on. No problems are solved in cylindrical or spherical coordinates. Given the limited scope of the tools required, there were still some problems which were quite challenging. The staff was always present to help with problems. Generally they gave just a hint or a nudge without divulging too much. The course tried some experimental formats for presenting and testing the material that they identified as such. Some such experiments failed (IMHO) but I consider that a minor drawback. Overall, this course does exactly what it purports to do, provide a solid review of basic mechanics.

The course was my first exposure to multivariable calculus and I have nothing to compare it to. So consider this the perspective of a multivariable newbie. Cons: 1) Buggy launch, but all that should be fixed the second time around. 2) Not enough. Not enough exploration of the implications of the material presented; not enough examples; not enough problems to solve. I finished feeling that my grasp of the material would be ephemeral and easily forgotten. Pros: 1) Minimal time spent passively watching videos, I like to interact ; ). 2) Wonderful, wonderful staff! They seem to genuinely want each and every student to understand and to pass. They were constantly on the forums answering questions. I only wish they had more help. 3) Python. Each section has optional assignments on Python programs applied to the math. This part of the course was minimally stressed but it was there for those who wanted to pursue it. It certainly adds to the richness of the course. Overall, it was an excellent course which, at my level, I found quite challenging.