MIT OpenCourseWare's 18.02 covers multivariable calculus: vectors, partial derivatives, multiple integrals, and vector calculus such as line and surface integrals. It is delivered as recorded MIT lectures with notes and problem sets.

Commenters call it an excellent, very good starting point for multivariable calculus and often pair it with 18.01 and 18.06 as free university-level material.

What commenters said (5)

1. Strongly recommendsekm22013in “Ask HN: Resources for Studying Multivariable Calculus?”

   MIT OCW Scholar has an excellent Multivariable Calculus class that i am currently self studying.

   http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable...

2. Recommendsjstx12022in “Ask HN: Text Book Recommendation for Math?”

   Don't read books, take classes instead - Khan Academy, MIT 18.01, 18.02, 18.06, Harvard Stat100 etc.

3. Recommendsjstx12021in “Ask HN: What's the best way to learn mathematics outside of formal education?”

   Take university classes - it's the same material, you just won't get any academic credits. MIT Opencourseware has Single Variable Calculus (18.01), Multivariable Calculus (18.02) and Linear Algebra (18.06). That's plenty of material to get started with. Watch the lectures, follow along with the textbook, do the exercises.

   If you're concerned that you don't have some of the prerequisites like high school algebra or trigonometry, Khan Academy have a pre-calculus course - start there.

   I switched to data science from an unrelated field and had to do a lot self-study like this to catch up on my math.

4. Recommendsst1x72020in “Ask HN: I want to teach myself Machine Learning. Where should I start?”

   I know that you've decided to take a gap year but my advice for next steps is actually to take undergraduate courses in single variable calculus, multivariable calculus, linear algebra and probability theory. All four of these are available online for free (course names: MIT 18.01, 18.02, 18.06, Harvard Stat110).

5. Recommendsb0ttler0cket2013in “Ask HN: Resources for Studying Multivariable Calculus?”

   1. I think the MIT response is a very good place to start, as I also used it (along with Khan) to do well during high school exams. I would also recommend as a further study aid

   (http://tutorial.math.lamar.edu/Classes/CalcIII/EqnsOfPlanes....).

   I recommend this site because of its concise outlines. MIT OCW is very video based and time consuming (not bad, just a fact). If you want pure, streamlined info (preview, review), then that's what I'm suggesting it for.

   2. In terms of a book (esp. a textbook), my experience is that the profusion of text is wearying. I did best when I study intensely for short bouts of time spread over a semester. I believe an outline is more conducive to this approach.

   3. As a source for problems to verify her knowledge and to practice the thinking method, I would recommend

   (http://people.math.gatech.edu/~cain/notes/calculus.html)

   I'll continue to look. To be honest, however, I have a feeling that the textbook has largely been replaced in favor of more readily accessible information online. Having one seems essential since it's the norm, but I think the online sites dedicated to teaching calculus3 are better suited.

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