Then the fifth chapter talks about differentiation in a now natural but objectively surprising way: we encounter the implicit function theorem and Lagrange multipliers, for example - not what you would generally find in an undergraduate analysis course.
This perspective and the attendant pedagogical strategy is illustrated by the sequence in which Edwards presents his topics: the first four chapters take the reader - or the student: this is a class-room text - from the basics of the theory of integration (in the indicated extended sense) to such differential geometric mainstays as Jacobians and the implicit function theorem. Edwards’ approach is to take calculus proper and present it in a truly advanced way, with the emphasis placed not so much on continuity and differentiability, as is the case with most undergraduate real analysis courses, but to build things up from the foundation of the integral as a linear functional acting on differential forms. The first edition of Advanced Calculus: A Differential Forms Approach, the book under review, appeared in 1969 as a somewhat unorthodox approach to undergraduate analysis: do it with an eye toward differential geometry, and, what is more, do it with differential geometry. It turns out, however, that Riemann’s Zeta Function is not his first book. Edwards wrote the book in 1974, pretty early in his career as a prolific author of books with a heavy historical dimension to them. Edwards as the author of the wonderful book Riemann’s Zeta Function, a marvelous work of historical scholarship and an exposition of the inner life of the zeta function, with the hypothesis on center stage. As I suppose is the case for many of us, I first encountered H.
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