Recommend me a super duper calc book

[TecHNooB]

B4 I die, Imma learn this stuff real good. The right way, not rote way. I need to be able to solve the hardest problems imaginable once I'm done (assuming I understand it all). Gimme your recommendations.

Edit: I just watched a bunch of videos about richard feynman and I'm thoroughly inspired

 

[ChuaChua]

Probably best to go look at University curricula and get their assigned textbook...

Are you looking for Calc I,II, III, IV?

 

[TecHNooB]

Probably best to go look at University curricula and get their assigned textbook...

Are you looking for Calc I,II, III, IV?

I'm looking for the definitive uber calc book that stresses the fundamentals, then rapes you with the most outrageous problems imaginable.

 

[rocadelpunk]

I'm looking for the definitive uber calc book that stresses the fundamentals, then rapes you with the most outrageous problems imaginable.

Before I can make a recommendation, have you ever done a proof before?

Which are you more interested in: proving why something works/formula exists or taking the end result and applying it.

In general the former is much more difficult and is what you would experience in an undergraduate mathematics degree. The applied side of things, depending on difficulty, is what you'd experience in your typical undergraduate core engineering/science classes

Judging from your post, I think you're a little misguided in what a difficult math problem is.

Addition
1+1=2 Easy

1.27845927457245284572458728045720457245807245 +2.38402738402734028340937840273402374203 Still easy, but time consuming.

The way you phrased your question it seems that you're looking for a bunch of those time consuming problems - which aren't necessarily difficult, they are still stressing the same fundamental ideas, but maybe just take longer/few more steps/requires a couple tricks...but really nothing exciting/new.

Anyway, what I'm trying to get at is your typical calc book will just ask you to understand the basic workings of the formula. The harder questions will just guide you to some "thought exercises/slightly deeper properties of the formulas

A book based on proofs wouldn't really have the typical word problem/application problems. It'd have you understand the proof of the formula (or have you prove it yourself) and then from that basic idea...what else can we come up/imagine?

Bottom line - do you want to think deeply about simple things or apply simple things to increasingly complex scenarios?

My recommendation would be for Spivak Calculus 3rd edition

 

[eLiu]

Adv Calc for Applications, 2nd:
http://www.amazon.com/Advanced-Calcu.../dp/0130111899

This book is pretty serious business, and it covers topics not seen in typical intro classes (like variations and I think differential forms) for that extra kick of fun. There are also some hard problems where 'hard' is applicable for almost any definition of hard.

For a more theory-oriented book, you can do no better than "Baby Rudin":
http://www.amazon.com/Principles-Mat.../dp/007054235X

That book is not f*cking around. The problems (all prove this, not compute this) are very challenging.

Also if you just want to see hard problems, go check out the Putnam math contest. The Putnam is not purely calculus problems, but every year there are a few. They come both in the form of "prove this" and "compute this". If you can solve these, you're a champ. Granted solving these problems is of little practical value, but they're hard & interesting nonetheless.

 

[firewolfsm]

For physics you can't beat the Feynmen Lectures on Physics. I suggest you read that and your calc book at the same time if you're interested.

 

[TecHNooB]

For physics you can't beat the Feynmen Lectures on Physics. I suggest you read that and your calc book at the same time if you're interested.

Plan on it Along with his other books. What an awesome dude.

 

[Cogman]

All the calculus that I've taken (thus far) has been out of the Thomas Calculus book http://www.amazon.com/Thomas-Calculu.../dp/0321185587

Its a pretty good book IMO, Most sections have a good mix of "easy problems to get the concept" to "Freaking hard problems for your enjoyment". generally, the concepts are well explained at the beginning of each chapter.

This only covers up to multi variable calculus (IE, Flux, greens therom, ect)

 

[MagnusTheBrewer]

There is no single best book. You need to review several to find one that teaches in the way you learn. Some concentrate on theory, proofs, problem solving or visual representation.

I might mention that there is a difference between rote learning and doing enough problems so you don't have to stop and think, "what next?"