A Course in Advanced Calculus

Nonfiction, Science & Nature, Mathematics, Calculus
Cover of the book A Course in Advanced Calculus by Robert S. Borden, Dover Publications
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Author: Robert S. Borden ISBN: 9780486150383
Publisher: Dover Publications Publication: September 11, 2012
Imprint: Dover Publications Language: English
Author: Robert S. Borden
ISBN: 9780486150383
Publisher: Dover Publications
Publication: September 11, 2012
Imprint: Dover Publications
Language: English

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.

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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.

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