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I'm a high school student who has just finished learning single variable calculus(or calculus-2). I want to study some elementary(to not overburden myself) multivariable calculus which would be very useful in understanding the heart of electrodynamics and magnetism. I do not want to learn this directly from books like Griffiths where only the necessary stuff for physics is taught(I want to enjoy the math obviously!).

I went through some standard books like Hubbard's and Spivak's but they're just way too advanced.

Is there any such elementary multivariable calculus book that you think is apt for me?

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  • $\begingroup$ Calculus: Early Transcendentals by Howard Anton, Irl Bivens, Stephen Davis, 10th edition is a great start. I'd recommend Calculus Volume 1 by Gilbert Strang as well. $\endgroup$
    – Jessie
    Feb 24, 2021 at 13:04
  • $\begingroup$ If you are looking for intuition on multivariate calculus in the physical perspective, a book I can't recommend enough is Div, Grad, Curl, and All That: An Informal Text on Vector Calculus. It might be a nice stopping point before entering texts like Spivak $\endgroup$
    – Rushabh Mehta
    Feb 24, 2021 at 13:13
  • $\begingroup$ There was a book called "How to Ace Calculus" which I thought was so-so. But the sequel "How to Ace the Rest of Calculus" I thought was quite good. The first author is Adams. The book is inexpensive and I think it's the level you're looking for. It pops right up on Amazon. 25 bucks. $\endgroup$
    – B. Goddard
    Feb 24, 2021 at 14:45
  • $\begingroup$ Thank you all for the amazing references! In particular I already started liking Div,Grad,...! $\endgroup$
    – newbie105
    Feb 24, 2021 at 16:45
  • $\begingroup$ In addition to Div, Grad, Gurl and All That mentioned elsewhere, I recommend Calculus of Several Variables by Serge Lang. $\endgroup$
    – Dave L. Renfro
    Feb 24, 2021 at 18:48

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First thing to understand is that there exists vectors calculus and multivariable calculus, both are related but not the same. The vector calculus is what you use in EM, in griffith for the first pages or so, he explains the basic vector calculus stuff but without really detailing the mathematics. If you just want physics, then just do griffith cover to cover.

There is another book for E&M by purcell, which is 'simpler' mathematically i.e: not requiring you to 'really' understand most of vector calculus results to approach E&M. However, this book's difficulty is that in the magnetism chapter, it uses concepts of relativity to bring in the connection between electricity and magnetism... which was sort of difficult for me to understand (And...also where I stopped reading this book )

It's not something too bad, because some of the techniques used in the book have no rigorous explanation like the method of separation of variable for solving partial differential equation.

In my profile bio, I've linked an animated video textbook which covers both multivariable and vector calculus. It is where I learned it, and I think it suffices for most part, but in that course too, a good knowledge of the basics is assumed. There is also a good YouTube channel called mu prime math which has playlists of short videos where you can understand the MV concepts.

It has it's pitfalls in that it doesn't give you problems to solve, but I guess you could search up individually search up problems to do or study some questions of integration on multiple integrations in MSE(There are many many solved examples on this site, you just have to look)

A great book is the one by Strang here, it has very nice pictures to aid in understanding the multivariable concepts.

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    $\begingroup$ That's funny - I found Strang outrageously hard, but the other resources mentioned and other textbooks were quite reasonable. I guess textbook preferences depend heavily on the person $\endgroup$
    – user404974
    May 7, 2021 at 22:23
  • $\begingroup$ What exactly is the difference between vector calculus and multivariable calculus? Is multivariable calculus the study of functions $\mathbb{R}^n \to \mathbb{R}$, while vector calculus is the study of functions $\mathbb{R}^n \to \mathbb{R}$? $\endgroup$
    – user56202
    Oct 25, 2021 at 16:05
  • $\begingroup$ @user56202 A very rough answer: vector calculus deals with (typically 3D) vector and scalar fields, and is a strict subset of multivariable calculus. $\endgroup$
    – ryang
    Jun 17, 2022 at 15:45
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Try Calculus by James Stewart.

An amazing book, with easy-to-understand explanations, and some really good intuitive exercises. Don't forget to solve the Problems Plus:)

But if you go a little short on exercise problems, you can opt for Demidovich.

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    $\begingroup$ Copyright laws vary from place to place. The link in the original version of this answer was to a website which violates the laws of some countries (most countries, even, as most countries are signatories to the Berne Convention). I have removed the link, as SE generally frowns on encouraging copyright violations (whatever the personal opinions of users or moderators might be on those issues). $\endgroup$
    – Xander Henderson ♦
    Feb 24, 2021 at 18:13

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