Global Calculus (Graduate Studies in Mathematics)

Ramanan (U. of California at Los Angeles) writes primarily for first-year graduate students interested in differential operations. Unlike most texts, this one begins by describing sheaves before differential manifolds, and then continues to an examination of connective algebra. Ramanan also takes a nontraditional approach to densities and orientations in which the change-of-variable formula is only a consequence. He follows this with descriptions sheaf cohomology connections, additional structures, the local theory of elliptic operators and finally the composition of vanishing theorems. Ramanan includes exercised throughout. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)