Acknowledged author Patrick M. Fitzpatrick wrote Advanced Calculus (Pure and Applied Undergraduate Texts: The Sally Series) comprising 590 pages back in 2009. Textbook and etextbook are published under ISBN 0821847910 and 9780821847916. Since then Advanced Calculus (Pure and Applied Undergraduate Texts: The Sally Series) textbook received total rating of 3.5 stars and was available to sell back to BooksRun online for the top buyback price of $29.14 or rent at the marketplace.
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.