
Preface  Table of Contents  Supplementary Material 
 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 selfcontained 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. An instructor's manual for this title is available electronically. Please send email to textbooks@ams.org for more information. Request an examination or desk copy. Readership Undergraduate students interested in teaching and learning undergraduate analysis. Reviews "This is a wellwritten and wellstructured book with clearly explained proofs and a good supply of exercises, some of them are quite challenging. It is this reviewer's opinion that the volume should be an excellent and useful tool for undergraduate students."  TeodoraLiliana Radulescu, Zentralblatt MATH 


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