Calculus, Second Edition, strikes a perfect balance between theory and technique. Although it differs from the majority of contemporary texts, treating integration before differentiation is the most accurate historical representation of the relationship between the integral and the derivative. This introduces the mean-value theorems and their applications earlier in the text, incorporates a treatment of linear algebra, and contains many new and easier exercises. As in the first edition, an interesting historical introduction precedes each important new concept.
We used this text for freshman and sophomore calculus. It is not a good introductory text for calculus, but is excellent for those who have already had some calculus. I hear that honors calculus classes used it years ago.
I never met Professor Apostle at Caltech. He was the standard freshman math lecturer, and I didn't take the standard sequence.