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Electronic ISBN:  9781470411145 
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Book DetailsPure and Applied Undergraduate TextsVolume: 1; 1998; 240 ppMSC: Primary 26;
Introduction to Analysis is designed to bridge the gap between the intuitive calculus usually offered at the undergraduate level and the sophisticated analysis courses the student encounters at the graduate level. In this book the student is given the vocabulary and facts necessary for further study in analysis. The course for which it is designed is usually offered at the junior level, and it is assumed that the student has little or no previous experience with proofs in analysis. A considerable amount of time is spent motivating the theorems and proofs and developing the reader's intuition. Of course, that intuition must be tempered with the realization that rigorous proofs are required for theorems. The topics are quite standard: convergence of sequences, limits of functions, continuity, differentiation, the Riemann integral, infinite series, power series, and convergence of sequences of functions. Many examples are given to illustrate the theory, and exercises at the end of each chapter are keyed to each section. Also, at the end of each section, one finds several Projects. The purpose of a Project is to give the reader a substantial mathematical problem and the necessary guidance to solve that problem. A Project is distinguished from an exercise in that the solution of a Project is a multistep process requiring assistance for the beginner student.
An instructor's manual for this title is available electronically. Please send email to textbooks@ams.org for more information.ReadershipUndergraduate students interested in learning analysis.

Table of Contents

Cover

Title page

Copyright

Preface

Contents

Chapter 0. Preliminaries

Chapter 1. Sequences

Chapter 2. Limits of functions

Chapter 3. Continuity

Chapter 4. Differentiation

Chapter 5. The Riemann integral

Chapter 6. Infinite series

Chapter 7. Sequences and series of functions

Index

Back Cover


Additional Material

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Introduction to Analysis is designed to bridge the gap between the intuitive calculus usually offered at the undergraduate level and the sophisticated analysis courses the student encounters at the graduate level. In this book the student is given the vocabulary and facts necessary for further study in analysis. The course for which it is designed is usually offered at the junior level, and it is assumed that the student has little or no previous experience with proofs in analysis. A considerable amount of time is spent motivating the theorems and proofs and developing the reader's intuition. Of course, that intuition must be tempered with the realization that rigorous proofs are required for theorems. The topics are quite standard: convergence of sequences, limits of functions, continuity, differentiation, the Riemann integral, infinite series, power series, and convergence of sequences of functions. Many examples are given to illustrate the theory, and exercises at the end of each chapter are keyed to each section. Also, at the end of each section, one finds several Projects. The purpose of a Project is to give the reader a substantial mathematical problem and the necessary guidance to solve that problem. A Project is distinguished from an exercise in that the solution of a Project is a multistep process requiring assistance for the beginner student.
An instructor's manual for this title is available electronically. Please send email to textbooks@ams.org for more information.
Undergraduate students interested in learning analysis.

Cover

Title page

Copyright

Preface

Contents

Chapter 0. Preliminaries

Chapter 1. Sequences

Chapter 2. Limits of functions

Chapter 3. Continuity

Chapter 4. Differentiation

Chapter 5. The Riemann integral

Chapter 6. Infinite series

Chapter 7. Sequences and series of functions

Index

Back Cover