The text is famous for its balance between rigorous proofs and physical applications. It covers the standard curriculum: vectors, differentiation in several variables, vector-valued functions, maxima and minima, multiple integrals, and the "Big Three" theorems (Green’s, Stokes’, and Divergence). The exercises range from routine checks of understanding to highly theoretical proofs that challenge even the most adept mathematicians.

| Aspect | Feedback | |--------|----------| | | Generally high — solutions are reliable | | Completeness | Often misses odd/even problems; some steps skipped | | Clarity | Can be terse; assumes you already understand the method | | Legality | Official versions are sold (not free PDFs); unauthorized PDFs violate copyright |

Double and triple integrals, change of variables, and applications to physics.