I just found this marvelous book and I think that it's the best book in this category, but I'm worried that it is not up-to-date. I've heard that Hardy's A Course of Pure Mathematics has some switched terms (It seems that the ideas are the same, but in Hardy's time, people used to call it with different terms) - although it's a great book too.
So, Is Courant's Introduction to Calculus and Analysis still up-to-date? The last printed edition was made by Springer in 1989 - I guess things didn't change much.