Real Analysis and Applications: Including Fourier Series and the Calculus of Variations

Frank Morgan has recycled most of his (somewhat) earlier book, Real Analysis, into 179 pages of text, including exercises, partitioned into 37 chapters.  He has deemphasized some parts of his other book's introductory chapters on real numbers, limits, and topology, separated out what seems to be the same three brief chapters on Fourier series, and added 12 chapters on various aspects of the calculus of variations.  Part V includes elegant expositions of minimal surfaces, optimal economic strategies, non-Euclidean geometry, and general relativity.

As in his previous book, the author declares in the Preface that "This text is designed for students."  But once again I am obliged to disagree.  There isn't enough detailed exposition of standard material in Morgan's text to make it a viable text for self-study.

Anyone teaching introductory analysis should read this book and be inspired by the expository gems within.  I am particularly impressed by the author's treatment of the calculus of variations.  However, it is not a text that many of us would choose to adopt for class use.

Henry Ricardo (henry@mec.cuny.edu) is Professor of Mathematics at Medgar Evers College of The City University of New York and Secretary of the Metropolitan NY Section of the MAA. His book, A Modern Introduction to Differential Equations, was published by Houghton Mifflin in January, 2002; and he is currently writing a linear algebra text.