Advanced Calculus

My first book had a perilous childhood. With this new edition, I hope it has reached a secure middle age. The book was born in 1969 as an „innovative text book“-a breed everyone claims to want but which usu ally goes straight to the orphanage. My original plan had been to write a small supplementary textbook on differen tial forms, but overly optimistic publishers talked me out of this modest intention and into the wholly unrealistic ob jective (especially unrealistic for an unknown 30-year-old author) of writing a full-scale advanced calculus course that would revolutionize the way advanced calculus was taught and sell lots of books in the process. I have never regretted the effort that I expended in the pursuit of this hopeless dream-{}nly that the book was published as a textbook and marketed as a textbook, with the result that the case for differential forms that it tried to make was hardly heard. It received a favorable tele graphic review of a few lines in the American Mathematical Monthly, and that was it. The only other way a potential reader could learn of the book's existence was to read an advertisement or to encounter one of the publisher's sales men. Ironically, my subsequent books-Riemann : S Zeta Function, Fermat: S Last Theorem and Galois Theory-sold many more copies than the original edition of Advanced Calculus, even though they were written with no commer cial motive at all and were directed to a narrower group of readers.