<p>Through a rigorous approach to the usual topics handled in one-dimensional calculus--limits, continuity, differentiation, integration, and infinite series--this text offers a deeper understanding of those concepts. The text is designed so that students come away from the course with a rigorous foundation for the basic topics of analysis. The exercise sets in this edition were expanded to give students additional opportunities for practice. Students are encouraged to pay particular attention to the exercises that have been marked with stars, because they are vital to the development of later sections. "Projects", appearing at the end of each chapter, present more challenging, multi-step problems.</p>

Introduction to Analysis

Science & Math

Edward D. Gaughan

Mathematics

Brooks/Cole

1984 Scott Foresman Algebra First Course (H) by Clyde L. Corcoran, Edward D. Gaughan, Norman E. Ladd, & Judith Salem ***ISBN-13: 9780673132802 ***596 Pages

Scott Foresman Algebra 1st Course

History

Clyde L. Corcoran

Norman E. Ladd

Judith Salem

Americas

Scott, Foresman Co.

<p>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 multi-step process requiring assistance for the beginner student.</p>

Introduction to Analysis (Pure and Applied Undergraduate Texts) (Pure and Applied Undergraduate Texts, 1)

American Mathematical Society

Orient Black Swan

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