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/sci/ - Science & Math

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11834148 No.11834148 [Reply] [Original]

What is the Best Calculus Book for someone with absolutely no experience?

>> No.11834180

>>11834148
watch the 3blue1brown videos for the broad concepts and pick up a more intermediate textbook for the proofs and techniques

>> No.11834185

>>11834180
>watch the 3blue1brown videos for the broad concepts
This but unironically.

>> No.11834187

>>11834148
Apostol is good

>> No.11834196

>>11834185
i just dont want him to get shit textbook that they would throw at american highschool students just because hes a total beginner

>> No.11834202

>>11834148
Spivak
I read Apostol vol.1. Madman starts with integrals. I like it, but it was tough
Spivak makes things easier.

>> No.11834233

>>11834148
I thought Stewart’s was pretty good.

>> No.11834256

>chadbrain tier: Apostol even though it’s a real analysis book instead of a calc book

>engineer tier: spivak

>midwit tier: Stewart

>complete fucking retard tier: anything else

>> No.11834289
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11834289

>>11834148
Follow my awful (ongoing) curriculum
https://learnaifromscratch.github.io/math.html

Eventually you get to a point where you can just work through all of Stewart's calculus (or Apostol's calculus, I learned from that book). Tao is a really good teacher, you will prove enough random shit with natural numbers that your mind will be rewired so when you read that Stewart book you can slay it and all it's exercises no problem.

>>11834187
I've read Vol 1 Apostol and many of the exercises are exceedingly difficult and tedious whenever he has nothing conceptual to add, he just tosses you trig identities to figure out, otherwise it probably is the best book to gain 'mathematical maturity' it's where I learned it from despite those endless tedious calculating exercises and sometimes impossible to follow proofs I had to look up elsewhere.
I shill for Tao now because he actually starts at the very beginning assuming no background

>> No.11834303

>>11834148
Read this whole book. It was good

>> No.11834363

>>11834289
> https://learnaifromscratch.github.io/
Is that course any good for a beginner?

>> No.11834393

>>11834148
baby rubin

>> No.11834404

Calculus made easy, it's the best introductory textbook to calculus

>> No.11834407

>>11834148
The Bible

>> No.11834459

>>11834148
You can either approach it and learn it with rigour or without. High school and non-math major uni calc would be examples of calc taught without rigour and Stewart's Calculus would be an okay book for that. Otherwise, you're going into proofs and would need something like Apostol or Spivak. I'm personally struggling through Apostol myself after having been through Stewart's in uni. If you're doing the latter, you could learn doing proofs from Book of Proof, Hammack or How to Prove It, Velleman.

>> No.11834477

>>11834148
Completing chapter 7 as I came across this thread. Stewart's is literally retard proof.

t. retard.

>> No.11834493

>>11834407
This, there's a lot of space in the margins to do calculation in, and the words don't mean anything so it's completely safe to write over them.

>> No.11834537
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11834537

>>11834407

>> No.11834548

>>11834537
They herded sheep, dumshit

>> No.11834559

Infinitesimal Approach by Keisler. Good for the most part, a few parts are poorly presented so if you get to something that doesn't make sense, cross reference Volume 1 by Apostol for the same content, but use Infinitesimal Approach as your main resource

>> No.11834564

>>11834256
Spivak is basically an intro to analysis and doesn't have any applications. How the fuck is it for engineers.
You never read any of those books
>>11834289
Analysis and Calc are different courses
It's fun but I'm not going to throw Tao or Rudin to some HS kid

>> No.11834683

OP here

So I read many of the suggestions and it's seems to be either
Spivak, Apostle, or Stewart

I took a look at Analysis 1 by Terrance Tao, and read the preface, ithe content was somewhat recognizable but when he talks about derivatives and integrals, I just have no clue,

Question: many of these books are Titled Calcalus, but as some of you have stated its more of an Analysis book, what is the difference? As far as I can see it seems Analysis requires knowledge of calculus beforehand, but then its contents include introduction to limits, which I thought was a intro to calc subject?

>> No.11834684

>>11834548
Yeah, that's what he said.

>> No.11834705

>>11834537
>>11834493
>haha the bible is so dumb LOL
>OMG I LOVE RICK AND MORTY IT'S SO DEEP AND RELATABLE

>> No.11834720
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11834720

>>11834705

>> No.11834750

>>11834705
>poorly reciting midwit onions man joke

>> No.11835552

>>11834148
Analysis 1 by Tao

>> No.11836308

Calculus for the practical man by J.E. Thompson has a lot of rigor and is relatively cheap. It is older and teaches in a different way than a college course but I feel like it better teaches the reasoning to the concepts

>> No.11836665

>>11834148
>James Stewart
Absolutely degenerate

>> No.11836670
File: 448 KB, 1590x2150, 81g4wK4y2EL.jpg [View same] [iqdb] [saucenao] [google]
11836670

>>11834148
I recommend reading the next two installments to this book as it proves very helpful for later.

>> No.11836677

>>11834683
Calculus is about learning theorems and how to use them to solve math problems, analysis is about rigorously proving the actual theorems.

A book like Apostol is more focused on proving the theorems as they’re introduced to you rather than using them, which is arguably more useful for a math major than a regular calculus course but utterly pointless and retarded and needlessly frustrating for engineers and the vast majority of students who take calc.

Stewart is basically the opposite, there’s no proofs at all besides for general explanation in the lessons and it’s entirely focused on using the theorems and rules to solve problems. Which is exactly what you’d want as an engineer.

Spivak is somewhere between the two I gather, ive never used it. But imo that may honestly be better for math majors as the learning curve in Apostol is pretty ridiculous for a freshman who’s never even taken an intro proofs class before

>> No.11837631

>>11834683
Don't start with Analysis books, they're for people who already know Calc and some math in general.
As for your question, yes they introduce limits. The difference is rigour and the level of the explanation. In introductory courses (and in books like Stewart) limits are defined as what the function approaches as the value considered approaches some other value. Then you're given the rules to work with them algebraically, same with differentiation and such.

In more rigourous books (Apostol, Spivak) you get this explanation but then you rigourously define what "approach" means, you derive the rules for algebraic operations, etc. Basically as the concepcts are introduced. (In stewart, for example, the rigorous definition of a limit is relegated to an appendix).

The problem sets in the books reflect this. Books like Stewart are more computational in nature to drill the patterns into you. The other books have some of this as well, but they also ask you to prove various statements, give you some more complicated problems, etc.
>>11836677
Spivak is absolutely not between the two, you "gathered" garbage. Apostol is rigurous and reads like a math textbook with theorem -> proof, etc but has a fair bit of applications and ties to the real world. Spivak is just straight pure math for the most part. It's a fun book though.

Also, engineers at my uni use Apostol in their first calc class

>> No.11837892

>>11834148
yes.