Following is an updated answer to that question that I originally posted to Quora. More of my answers are available here.
The Feynman Lectures are better for an already educated student to review and further grasp basic physics. The Feynman Lectures wouldn’t be my first choice of books for a beginning physics student. But I assume that’s the spirit in which this question is asked. So what’s a great book for a beginning calculus student to try to master the subject?
I recommend Calculus Made Easy by Silvanus Thompson. It was originally published in 1910, so it’s in the public domain. The prologue gives you a flavor for Thompson’s engaging and unpretentious writing style:
Considering how many fools can calculate, it is surprising that it should be thought either a difficult or a tedious task for any other fool to learn how to master the same tricks.Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the textbooks of advanced mathematics – and they are mostly clever fools – seldom take the trouble to show you how easy the easy calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way.Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool can do, another can.
Complete text from Project Gutenberg, here: http://www.gutenberg.org/
There’s also a more recent edition available from Amazon. Noted mathematical writer, Martin Gardner, revised and updated Thompson’s classic text.
