What's the most comprehensive, industry-standard textbook on single and multi-variable calculus?

What's the most comprehensive, industry-standard textbook on single and multi-variable calculus?

Here's the deal. I'm a 31-year-old lawyer by trade, but my lifelong interests include physics, compsci, and sysadmin stuff. I probably spend 5-7 hours a week in independent study.

I read Griffiths' Electrodynamics last year, and this year I'm working through the Feynman Lectures. Unfortunately, I'm pretty rusty at calculus, which is the main reason I'm now struggling -- I just don't see how Feynman solves some of his equations.

Money is no object, and I can handle difficult material (as long as it starts from ground zero, I can handle a fast pace). I used to be pretty good at calc, and got good grades in college. I've forgotten much of it over the decades, but much of this still won't be totally new to me. I still know basic integrals, Green's Theorem, Stokes' Theorem, etc., but I'm rusty as fuck.

Any recommendations? I'm a textual learner, so lectures and videos won't do much for me.

Steward's Early trascendals
Pretty much every day Calculus college student uses it for both Calc 1 and 2.
Plus, you can easily find free PDF versions online.

Thanks, man. Much appreciated.

Unless anyone disagrees, I suppose I'll go with that.

Either Apostol, Courant, or Spivak, or go home.

>Stewart's Calculus
Nigga pls, that soft, unrigorous mammoth will get you nowhere.

stewart's calc is pretty terrible.. i think the only reason universities sell them is because they're expensive

>unrigorous
proof?

Well, since it is your life's interests I do recommend one of the autist-core Calc books like said. Stewart is good for the basics, it's not really in depth.

>proof?
If you even had to ask this then you will never make it in pure maths

Sorry bub, why don't you try something like bee-keeping instead?

Can vouch for that, using Stewart's in my calc 1 class this term. I pretty much just use it as a source of problems to do.

very bad. disorganized. little proof. body doesn't always do a good job at preparing you for questions, yet still manages to not cover very much ground.

I would guess spivak, though unfortunately I never went back and re-learned calc from a better book since I did well in the class.

The only thing Stewart has going for it is the amount of topics covered along with the ungodly amount of problems it has.
Then again if it is practice problems you want, Spivak has a good amount, they are pretty challenging and fun as well.

People on Veeky Forums don't seem to understand this distinction, so I'm going to explain it.

Stewart is a book aimed at people who want to apply Calculus in fields outside of mathematics. It is a good book if your primary interest is physics, engineering, economics, or anything else that uses Calculus for real world application.

Spivak is a book aimed at people who want to do proof based mathematics. It's a great book for people who want to begin learning proofs by making Calculus rigorous, and also serves as a way of getting into the field of mathematical analysis. It is a book for aspiring mathematicians, and other people who use proofs.

Despite both having the title "Calculus", they aim to do entirely different things, and are both excellent books for their target audience.

OP, based on your post, you're looking for an application based perspective. In that case, I would recommend Stewart. That said, if you've never studied proofs in your life, you should consider looking into it, and Spivak would be a great place to start. I will add that logic argument (which may have drawn you to be a lawyer, depending on what you do), is central to mathematics, whereas it is far less important in other fields.

This nigga speaks truth OP

Guy with a physics degree here.

I want to re-study calculus from a more rigorous perspective. I'd like it to be comprehensive too.

Which is better, Courant or Apostol?

Try KhanAcademy it's pretty good

Spivak. This is especially the case if you've never done proofs before.

Courant is fairly old. Apostol is a bit more dry and less explanatory. This is good if you like less exposition and and more straight content, and you already know proofs. However, it is problematic if you don't know proofs, or if you want a text which is actually explanatory.

Beyond this, I like the exercises in Spivak a lot more.

Spivak is going to give you a comprehensive look at the rigor behind single variable calculus, as well as sequences and series. After this, there are a lot of places you might go depending on what you want. Calculus on Manifolds is the book for multivariable calculus (building up to Stoke's Theorem), and it may also be worthwhile to learn some other parts of analysis. Baby rudin is usually suggested here, but be warned it's not for the faint of heart. You may also consider some books on linear algebra, in which case I would recommend Axler's Linear Algebra Done Right.

I'm glad to hear you're brushing up on the material, but was Griffiths' really at a low enough level to not require mastery of basic multivariable calculus? You might want to revisit it unless you were just reading for content versus actually being able to apply the methods/solve electromagnetic physics problems.

As for the thread topic, I taught myself using Paul's Online Notes (look up Paul's Online Notes Calc III) before going into undergrad. It covers pretty much everything you'll need in a standard multivariable calculus course and has a few good examples to see some of the procedures applied concretely. The only things it won't touch are the areas you start to see in a rigorous mathematics course on analysis, multivariable analysis, and eventually differential geometry.

Feynman lectures shouldn't use anything more advanced than whats contained in Paul's Online Notes or Stewart.

>Spivak
>comprehensive
Ayy lmao.

But seriously, I read that book freshman year and it barely covered anything within calculus. It's an intro to analysis book, and definitely shouldn't be used as a general text.

That's why I was trying to decide between Courant and Apostol.

In that case, just read an analysis book like Rudin.

>courant or apostol?
>>spivak
>courant or apostol?
>>baby rudin
I feel like we're missing something here.

Morris Klines "Calculus: A physical Approach"

I highly recommend this to dust off the cobwebs, he's very descriptive.

His proofs are also a joy to follow. It's almost like a story.

Apostol and Courant cover ground at about the same pace as Spivak. They're just much longer books. I guess if I had to go with something for you, probably Apostol. That said, you'd get more out of a real analysis book.

If you really can't decide, just go to libgen.io and flip start reading, see what appeals and what doesn't.

Apostol and Courant cover ground at about the same pace as Spivak. They're just much longer books. I guess if I had to go with something for you, probably Apostol. That said, you'd get more out of a real analysis book.

If you really can't decide, just go to libgen.io and just start reading, see what appeals to you.

Well don't get me wrong. I've read Apostol's Analysis and baby Rudin. I don't need to brush up on Bolzano Weierstrass, series, or what an open cover is.

My main need is a comprehensive, rigorous review of all calculus as it pertains to physics. So not really analysis and the longer the better.

Also, would you consider Courant to be outdated? I had actually suspected the opposite, since some Amazon reviewers mentioned "strange notation" in Apostol.

Manfredo :p

I guess it's really just the prose. Courant lived from 1888-1972, whereas Apostol lived from 1923-2016. Even though they were written at similar times, Courant "feels" older to me when I read him.

Old, but highly recommended.

You mentioned you read Griffiths E&M. The vector calculus appendix is actually quite good, the best I've seen in a physics text in fact.