About Book:

     This is a textbook for a one-year course in analysis designed for students who have completed the ordinary course in elementary calculus. I hope that this book can enable the student to learn enough examples, theorems, and techniques it, analysis to be well prepared for the standard graduate courses in general topology, measure theory, and functional analysis.

     The material presented represents a departure from that usually given in traditional “advanced calculus” courses. In addition to fundamental material on sequences, series, and differential and integral calculus of functions of one variable, I take up topics ordinarily reserved for more advanced “real variable “courses. Two important examples of such topics are metric spaces and Lebesgue integration.

     Also treated are several smaller but interesting topics which are often neglected I the undergraduate curriculum, for example, Baire category and discontinuous functions, and summability of sequences and series.

On the other hand I do not deal at all with calculus of functions of several variables. Such topics as differentials and vector calculus can now be best understood from the point of view of modern differential geometry.  For this reason I believe they should be taught in a separate course.