About the Book

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. A considerable amount of time is spent motivating the theorems and proofs and developing the reader’s intuition. 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.