I am a pre-engineering student currently taking a Single Variable Calculus course at a community college.
I recognize that my future success (or not so much) as an engineer will be based, in large part, on my capabilities with and understanding of Calculus. Therefore, I really, really want to master it like I've never mastered any subject before.
I'm doing well in my class, and my instructor is great, but I am under the impression that this course and it's textbook (Calculus, Early Transcendentals by Stewart) do not delve quite as deeply into Calculus as I would like. Also, the textbook frequently introduces new techniques and concepts with little to no explanation.
(Incidentally, I'm a self-taught software developer, so I am adept at learning new topics on my own. Learning Mathematics is, IMHO, quite similar to learning a new programming language.)
So I'm hoping to find some really excellent Calculus textbooks that will give me deep insight into the topics of differentiation and integration (and any other topics my course may be missing).
I've used Google and my school's library to search extensively, and I've found no shortage of Calculus textbooks. My problem is that, since I'm just now learning the basics, I have no way to know just how in-depth an advanced or in-depth book should go, or what important information my current textbook may be missing.
I own a copy of The Calculus Lifesaver, by Adrian Banner, which is absolutely outstanding. If anyone reading this happens to be struggling with Calculus, this is the book to turn to.
I also have been taking advantage of the Calculus courses in MIT's OpenCourseware. Calculus Revisited, with Herbert Gross, has been very helpful. His way of explaining the concepts just really "clicks" with me.
So, with that said, I'm just hoping the experts in the community here can recommend some great resources (e.g. books, free online courses, or other media) to help me optimize my knowledge of Calculus.
Thanks in advance!
Best Answer
From what I gather the holy grail of calculus books seems to be Calculus by Micheal Spivak.