Foundations of analysis
 Responsibility
 Joseph L. Taylor.
 Language
 English.
 Publication
 Providence, Rhode Island : American Mathematical Society, [2012]
 Copyright notice
 ©2012
 Physical description
 x, 398 pages : illustrations ; 27 cm.
 Series

Pure and applied undergraduate texts ; 18.
Sally series (Providence, R.I.)
Access
Creators/Contributors
 Author/Creator
 Taylor, Joseph L., 1941
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Publisher's Summary
 Analysis plays a crucial role in the undergraduate curriculum. Building upon the familiar notions of calculus, analysis introduces the depth and rigor characteristic of higher mathematics courses. Foundations of Analysis has two main goals. The first is to develop in students the mathematical maturity and sophistication they will need as they move through the upper division curriculum. The second is to present a rigorous development of both single and several variable calculus, beginning with a study of the properties of the real number system. The presentation is both thorough and concise, with simple, straightforward explanations. The exercises differ widely in level of abstraction and level of difficulty. They vary from the simple to the quite difficult and from the computational to the theoretical. Each section contains a number of examples designed to illustrate the material in the section and to teach students how to approach the exercises for that section. The list of topics covered is rather standard, although the treatment of some of them is not. The several variable material makes full use of the power of linear algebra, particularly in the treatment of the differential of a function as the best affine approximation to the function at a given point. The text includes a review of several linear algebra topics in preparation for this material. In the final chapter, vector calculus is presented from a modern point of view, using differential forms to give a unified treatment of the major theorems relating derivatives and integrals: Green's, Gauss's, and Stokes's Theorems. At appropriate points, abstract metric spaces, topological spaces, inner product spaces, and normed linear spaces are introduced, but only as asides. That is, the course is grounded in the concrete world of Euclidean space, but the students are made aware that there are more exotic worlds in which the concepts they are learning may be studied.
(source: Nielsen Book Data)
Subjects
 Subject
 Functional analysis.
 Functions of real variables.
 Real functions  Instructional exposition (textbooks, tutorial papers, etc.)
 Real functions  Functions of one variable  Functions of one variable.
 Real functions  Functions of several variables  Functions of several variables.
 Real functions  Inequalities  Inequalities.
 Mathematical logic and foundations  Set theory  Set theory.
Bibliographic information
 Publication date
 2012
 Series
 Pure and applied undergraduate texts ; 18
 Sally series
 ISBN
 9780821889848 (alk. paper)
 0821889842 (alk. paper)