Mathematical Analysis: An Introduction

by Andrew Browder

Among the traditional purposes of such an introductory course is the training of a student in the conventions of pure acquiring a feeling for what is considered a proof, and supplying literate written arguments to support mathematical propositions. To this extent, more than one proof is included for a theorem - where this is considered beneficial - so as to stimulate the students' reasoning for alternate approaches and ideas.
The second half of this book, and consequently the second semester, covers differentiation and integration, as well as the connection between these concepts, as displayed in the general theorem of Stokes. Also included are some beautiful applications of this theory, such as Brouwer's fixed point theorem, and the Dirichlet principle for harmonic functions. Throughout, reference is made to earlier sections, so as to reinforce the main ideas by repetition. Unique in its applications to some topics not usually covered at this level.

Genres: Mathematics

349 pages, Hardcover

First published December 15, 1995

Reviews

[Pat · Rating 3 out of 5]

:( it's not fun reading this book but it gets the job done (some sections will leave a bit out). suffers from a lack of examples. but at least the exercises were very fun to do! first semester was set theory, quick review of single variable analysis, topology, function spaces, differential calculus, and the beginning of the section on manifolds. second semester was measure and integration theory (in just the first half before going to a different book).

historical notes at the end of each chapter are interesting.