So school is slowing down. I’m not getting a whole lot of homework and I was wondering if anyone had recommendations for any calculus textbooks that they could recommend that would be fun to read. A few friends have recommended calculus by Spivak. I’m currently in BC Calculus and find it exceedingly boring because of the slug-like pace we go at. Thoughts? Additionally, could anybody recommend me places to get the textbooks for cheap? Thanks in advance!
Also, online courses could be pretty cool too. If you have any recommendations for those that would also be greatly appreciated
The Spivak and Apostol books would be good for a more theory based approach. You can also look for the course home pages for courses like Caltech Ma 1a.
If you just want a free regular calculus book, the Strang book is on the web at MIT Open Course Ware (along with an associated course).
Recommendation: Spivak’s Calculus 
For theoretical (more pure mathy):
Spivak, Apostol, Courant, Baby Rudin, G. H. Hardy
Spivak from my experience is the most interesting and highly recommend it ^^. Apostol is a bit dry but more detailed.
Baby Rudin is a huge jump and personally won’t recommend it at start. And Courant and Hardy’s Course in Pure Math, well… it’s the other of the 5 highly recommended which I had never experienced so no comments.
For regular Calculus books:
Personally, not Stewart ever (unless you are into computational and don’t really care about the theoreticals. I just personally don’t think this is a good book and many high school AP Calc are superior in quality)
MIT like ucbalmus says has free textbook
Other universities have free books as well like Old Dominion Univ, UW-Madison, Whitman, Harvard, Smith
Just google for free calculus books with filetype:pdf
Should filter quite a chunk of unnecessary links. Also, AP Calc BC is Calc I, and Calc II. But personally, I would recommend reviewing Calc II before college if you plan on not going pure math and if you are going pure math, Spivak!
Also…
Places to get it for cheap:
- the web
- your local library
Keep in mind that Strang gets right into the derivative…at least in the textbook that I have…from the jump. Overall, Strang approach is great considering that his specialty is linear algebra.
If you mean Rudin’s Principles of Mathematical Analysis, that book is usually used for junior-level real analysis courses.
And I had a high school friend who went right into Baby Rudin and didn’t face much trouble.
Depends on the learning curve I guess.
I did write that it was a huge jump as even I would not have been able to have done it before college.
Plus, I recommended Spivak, not Baby Rudin.
(I mean technically, Baby Rudin is Calculus… (though it’s often referred to as introduction to modern analysis and was also used in my analysis course))
Most of the mass market textbooks are basically highly similar in content and information. All of them have their flaws, though, and it really depends on what your teacher and you’d like to emphasize more. I’ve tutored with some different books (Stewart and Rogawski) to supplement the current book our department uses (Ron Larson’s Calculus, pretty mainstream.)
I don’t recommend anyone trying to jump into analysis after taking a semester of calculus, but it’s possible. To my knowledge, it’s an upper-division requirement in all of the undergrad math programs, and you should at least get familiar with some proofs before you attempt to prove some of the Bolzano-Weierstrass theorems, for instance.
Amazon is obviously the best places to get a cheap textbook from. Early editions (obviously used copies) are pretty job and sometimes no more than $20.
Recommendation: Rogawski’s Calculus, any edition.