Advanced Calculus

Patrick Fitzpatrick

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ISBN 10: 0821847910 ISBN 13: 9780821847916

Published by American Mathematical Soc., 2009

Language: English

Condition: Used - Good Hardcover

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This is the 2nd Edition of 'Advanced Calculus' by Patrick Fitzpatrick, an essential text for undergraduate courses in mathematical analysis. Published by the American Mathematical Society, this book rigorously presents fundamental concepts through clear examples and exercises, covering topics from single-variable calculus to differential calculus in Euclidean spaces. This specific copy is in good condition, featuring clean, unmarked pages and a tight binding, making it an excellent resource for students and professionals. It is a self-contained text, perfect for building a strong foundation in analysis.

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Bibliographic Details

Title: Advanced Calculus
Publisher: American Mathematical Soc.
Publication Date: 2009
Language: English
ISBN 10: 0821847910
ISBN 13: 9780821847916
Binding: Hardcover
Edition: 2nd Edition.
Condition: Good

About this title

Synopsis

Advanced Calculus is intended as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis. The goal is to rigorously present the fundamental concepts within the context of illuminating examples and stimulating exercises. This book is self-contained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrability, 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.

About the Author

Patrick M. Fitzpatrick is Professor and Chair of Mathematics at the University of Maryland, College Park.

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