Spivak's Calculus

Rudin's Principles

Its very basic material but some of the problems are very challenging. Overall its about the same difficulty as Rudin in terms of problem difficulty but of course Rudin is more abstract and formal.

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>>8537005
Honors level for calculus
Remedial level for analysis

>>8537005
It's an awful book precisely because it attempts to be both a Calculus book and Analysis book at the same time, yet fails to be either. Courant and John is a much superior alternative, although a lot harder.

>>8537034
Theres rather minimal difference. Spivak is really only missing a referal to topological structures that are all pretty trivial to comprehend.

Where should I look to do review/practice problem for all calcs?

>>8537066
Stewart's Calculus or Paul's Online Notes

In my uni, spivack is really the norm when teaching calculus (except for C.S. Brainlets who don't even have calculus courses lol). Though most teachers recommend to look on other textbooks for reviewing concepts. The thing is, spivack problems are pretty challenging and involve proofs which many professors here prefer we learn over pure application. However, if you actually try to understand the underlying concepts and skills this sort of treatment gives you, application/crunching problems will come naturally and quite easily. Though it's always wise to keep practicing.

>>8537014
> Courant and John

Holy shit. Fucking THANK YOU

I thought Spivak was the gold standard but I'm a few pages into this and I think I'm gonna drop Spivak for the time being. This seems much more useful in real world terms.

>>8537005
one thing I noticed about this book is the use of "her" and "she" when referring to a third person.

what is this? cuckulus?

>>8537166
Holy kek, Keith Devlin does this as well.
The preface of They Joy of Sets cracked me up. Kuck Devlin.

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>>8537197
>Broof.

>>8537207
>assuming someone's gender
Binned.

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He assumes the reader is cis-gender. I am triggered.

>>8537166
This is what differentiates good math books from the bad math books. You can tell Spivak is a cuck about 4 chapters in. Reading any further than that you're effectively prepping the bull subconsciously, permanently affecting your abilities. I legitimately believe this.

>>8537104
Hello there fellow U of T person.

>>8537207
He should've added, for now on you can refer to this classification as spivak pronouns.

>>8537197
I'm assuming he's just trying to cover his ass in case some feminist cunts get triggered and try to sue him for writing "he"

Can someone here elaborate on the substantial difference between calculus and analysis? In Italy we only have analysis because of strong tradition in the field, I guess calculus is a part of analysis but I'm just imagining.

>>8537320
Briefest way I can put it is calculus is analysis when the only space you consider is R^n

>>8537320
As I understand it calculus is basically just differentiation and integration. Correct me if I'm wrong.

>>8537374
Some limits too
Basically calculus is shut up and calculate, whereas analysis trys to build up ideas from simpler ideas

>>8537320
In europe you call both Calculus and Analysis by "Analysis". That doesn't mean it is.

Difference: After taking a first course in analysis you should understand the concepts of compacity, its equivalence to closed/bounded, lipschitz functions, uniform continuity, etc etc.

>>8537347
It's really not that. Everything I said applies to R^n and you won't see it in any calculus class. Neither will you see R^n-specific things like inner product inequalities, equivalence of all norms, etc.

>>8537005
If you're trying to learn calculus Spivak is the best you can get, and it's supposed to be hard. If you're trying to learn analysis, Spivak isn't going to cut it, and you're better off reading a real analysis book. I recommend Terence Tao's Analysis I. Very light and friendly, information-dense, and intended to guide newcomers into math (it's still going to be hard).

>>8537320
It depends on how on depth your calc course was. But in many cases calculus is just a way to learn a collection of methods to solve problems dealing with change and other shit like that. In some cases, you take something pretty close to analysis (that means you construct the reals and go from there trying to prove everything you can), but still focus in learning the methods. Or some profesors literally teach analysis, they just never mentioning that what you already proven is valid for other topological/vector/metric/inner product spaces because they don't want to be nagged by the faculty department. But to be concise, calculus mainly deals with the way to solve these sort of problems while analysis is s way to rigorously construct everything you use in calculus (that doesn't mean analysis is useless, but your motivation for studying it shouldn't be purely pragmatic).

Hope this helps.

>>8537561
*rigorously construct and generalise. The latter is important because some proofs don't eveb mention the fact that you are using the reals and work for other fields or vector spaces.

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>>8537232
i hope this isn't ironic

Stewarts calculus if you don't know calculus, if you do there are other advanced calculus textbooks.

>>8538143
I didn't know any calculus before starting Spivak. Steward has shit reviews.

>>8538157

>Stewart has shit reviews

You got memed my friend.