Synopses & Reviews
This remarkable undergraduate-level text offers a study in calculus that simultaneously unifies the concepts of integration in Euclidean space while at the same time giving students an overview of other areas intimately related to mathematical analysis. The author achieves this ambitious undertaking by shifting easily from one related subject to another. Thus, discussions of topology, linear algebra, and inequalities yield to examinations of innerproduct spaces, Fourier series, and the secret of Pythagoras. Beginning with a look at sets and structures, the text advances to such topics as limit and continuity in En, measure and integration, differentiable mappings, sequences and series, applications of improper integrals, and more.
Carefully chosen problems appear at the end of each chapter, and this new edition features an additional appendix of tips and solutions for selected problems.
Synopsis
This excellent undergraduate calculus text offers students an unusual perspective on concepts of integration in Euclidean spaces and their relationship to other mathematical areas. Subjects include sets and structures, limit and continuity in En, measure and integration, differentiable mappings, sequences and series, applications of improper integrals, and more. Preface. Problems. Problems with tips and solutions for some.
Synopsis
This remarkable undergraduate-level text offers a study in calculus that simultaneously unifies the concepts of integration in Euclidean space while at the same time giving students an overview of other areas intimately related to mathematical analysis. Carefully chosen problems appear at the end of each chapter. This new edition includes an additional appendix of tips and solutions for selected problems.
Synopsis
An excellent undergraduate text examines sets and structures, limit and continuity in En, measure and integration, differentiable mappings, sequences and series, applications of improper integrals, more. Problems with tips and solutions for some.