Linear analysis · linear spaces · linear transformations and matrices · determinants · eigenvalues and eigenvectors · eigenvalues of operators acting on euclidean spaces · linear differential equations · systems of differential equations · nonlinear analysis · differential calculus of scalar and vector fields · applications of the differential calculus · line integrals · special topics · set functions and elementary probability · calculus of probabilities · introduction to numerical analysis
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.