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(More customer reviews)In this textbook the authors have provided an important classroom tool for teaching undergraduates introductory real analysis. Without sacrificing rigor, they treat all the classical topics and principal theorems (convergence of sequences, limits and continuity of functions, differentiation, integration) in a lucid manner by exploiting the elementary machinery of sequences. This approach, free from the technical abstractions of general topology, makes the book much more readable for the average junior/senior level student majoring or minoring in mathematics. I have used the book for a one-semester course, and I don't think I would revert to the standard topological method for ordinary students in a first course in real analysis. Some of the main results can be re-derived as corollaries in a follow-up course on point-set topology for students interested in attending graduate school.
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Completely revised and updated, the second edition of An Introduction to Analysis presents a concise and sharply focused introduction to the basic concepts of analysis from the development of the real numbers through uniform convergences of a sequence of functions, and includes supplementary material on the calculus of functions of several variables and differential equations. This student-friendly text maintains a cautious and deliberate pace, and examples and figures are used extensively to assist the reader in understanding the concepts and then applying them. Students will become actively engaged in learning process with a broad and comprehensive collection of problems found at the end of each section.
