ISBN 9780821852095,Advanced Calculus

Advanced Calculus



Universities Press

Publication Year 2010

ISBN 9780821852095

ISBN-10 0821852094


Edition 2nd
Number of Pages 608 Pages
Language (English)


This book is self-contained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrality, and power series representation properties of functions of a single variable are established. The next few chapters describe the topological and metric properties of Euclidean space. These are the basis of a rigorous treatment of differential calculus (including the Implicit Function Theorem and Lagrange Multipliers) for mappings between Euclidean spaces and integration for functions of several real variables. Special attention has been paid to the motivation for proofs. Selected topics, such as the Picard Existence Theorem for differential equations, have been included in such a way that selections may be made while preserving a fluid presentation of the essential material. Supplemented with numerous exercises, Advanced Calculus is a perfect book for undergraduate students of analysis.

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