Incluye índice.

1. Limits, continuity, and compactness -- 1.1 Number systems and the principle of mathematical induction -- 1.2 A quick introduction to cardinal numbers -- 1.3 Limits -- 1.4 Vector space, metric space, norms, and inequalities -- 1.5 Continuous functions, open, closed, and compact sets in Rn

2. Differentiation on Rn -- 2.1 Differentiability on Rn -- 2.2 Higher partial derivatives and Taylor's theorem -- 2.3 Maxima and minima for real valued functions of several variables -- 2.4 The implicit function theorem

3. One and several dimensional integral calculus -- 3.1 Brief review of integrals of real-valued functions defined on a finite closed interval in R -- 3.2 Curves, arc length, and line integrals -- 3.3 Higher dimensional integrals -- 3.4 Multiple integrals and their reduction to one dimensional integrals -- 3.5 Green's theorem -- 3.6 Integration on surfaces

Authors' biographies -- Index.

This book assumes the students know some of the basic facts about Calculus. We are very rigorous and expose them to the proofs and the ideas which produce them. In three chapters, this book covers these number systems and the material usually found in a junior-senior advanced Calculus course. It is designed to be a one-semester course for talented freshmen. Moreover, it presents a way of thinking about mathematics that will make it much easier to learn more of this subject and be a good preparation for more of the undergraduate curriculum.