Advanced Calculus

"e;This book is a radical departure from all previous concepts of advanced calculus,"e; declared the Bulletin of the American Mathematics Society, "e;and the nature of this departure merits serious study of the book by everyone interested in undergraduate education in mathematics."e; Classroom-tested in a Princeton University honors course, it offers students a unified introduction to advanced calculus. Starting with an abstract treatment of vector spaces and linear transforms, the authors introduce a single basic derivative in an invariant form. All other derivatives — gradient, divergent, curl, and exterior — are obtained from it by specialization. The corresponding theory of integration is likewise unified, and the various multiple integral theorems of advanced calculus appear as special cases of a general Stokes formula. The text concludes by applying these concepts to analytic functions of complex variables.