Your Waterstones card is changing, introducing...
Mathematical Analysis: An Introduction - Undergraduate Texts in Mathematics (Hardback)
  • Mathematical Analysis: An Introduction - Undergraduate Texts in Mathematics (Hardback)

Mathematical Analysis: An Introduction - Undergraduate Texts in Mathematics (Hardback)

Hardback 335 Pages / Published: 25/01/2001
  • We can order this

Usually despatched within 3 weeks

  • This item has been added to your basket
Among the traditional purposes of such an introductory course is the training of a student in the conventions of pure mathematics: 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.

Publisher: Springer-Verlag New York Inc.
ISBN: 9780387946146
Number of pages: 335
Weight: 1490 g
Dimensions: 235 x 155 x 20 mm
Edition: 1st ed. 1996. Corr. 3rd printing 2001


This is a very good textbook presenting a modern course in analysis both at the advanced undergraduate and at the beginning graduate level. It contains 14 chapters, a bibliography, and an index. At the end of each chapter interesting exercises and historical notes are enclosed.\par From the cover: ``The book begins with a brief discussion of sets and mappings, describes the real number field, and proceeds to a treatment of real-valued functions of a real variable. Separate chapters are devoted to the ideas of convergent sequences and series, continuous functions, differentiation, and the Riemann integral (of a real-valued function defined on a compact interval). The middle chapters cover general topology and a miscellany of applications: the Weierstrass and Stone-Weierstrass approximation theorems, the existence of geodesics in compact metric spaces, elements of Fourier analysis, and the Weyl equidistribution theorem. Next comes a discussion of differentiation of vector-valued functions of several real variables, followed by a brief treatment of measure and integration (in a general setting, but with emphasis on Lebesgue theory in Euclidean spaces). The final part of the book deals with manifolds, differential forms, and Stokes' theorem [in the spirit of M. Spivak's: ``Calculus on manifolds'' (1965; Zbl 141.05403)] which is applied to prove Brouwer's fixed point theorem and to derive the basic properties of harmonic functions, such as the Dirichlet principle''. ZENTRALBLATT MATH

A. Browder

Mathematical Analysis

An Introduction

"Everything needed is clearly defined and formulated, and there is a reasonable number of examples.... Anyone teaching a year course at this level to should seriously consider this carefully written book. In the reviewer's opinion, it would be a real pleasure to use this text with such a class."-MATHEMATICAL REVIEWS

You may also be interested in...

Calculus for the Ambitious
Added to basket
Schaums Outline of Tensor Calculus
Added to basket
Added to basket
How to Think About Analysis
Added to basket
Quick Calculus
Added to basket
Introduction to Complex Analysis
Added to basket
Schaum's Outline of Calculus
Added to basket
Ordinary Differential Equations
Added to basket
Calculus Essentials for Dummies
Added to basket
Schaum's Outline of Vector Analysis
Added to basket
Added to basket
A Brief Guide to the Great Equations
Added to basket


Please sign in to write a review

Your review has been submitted successfully.