000			03453nam a22003257a 4500
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005			20240610115346.0
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020			_a9781470425791
040			_aNISER LIBRARY _beng _cNISER LIBRARY
041			_aEnglish
082			_a517 _bTAY-F
100			_aTaylor, Joseph L.
245			_aFoundations of analysis
260			_aHyderabad : _bUniversities Press, _c2016.
300			_ax, 398p. ; _c27 cm.
490			_aPure and applied undergraduate texts ; _v18
504			_aIncludes bibliographical references (page 387) and index.
520			_aAnalysis 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.
650			_aFunctional analysis.
650			_aFunctions of real variables.
650			_aReal functions -- Instructional exposition (textbooks, tutorial papers, etc.).
650			_aReal functions -- Functions of one variable -- Functions of one variable.
650			_aReal functions -- Functions of several variables -- Functions of several variables.
650			_aReal functions -- Inequalities -- Inequalities.
650			_aMathematical logic and foundations -- Set theory -- Set theory.
856			_3Table of Content _uhttps://www.ams.org/bookstore/pspdf/amstext-18-toc.pdf?_gl=1*pvcq4c*_ga*OTY4OTA1OTY3LjE3MTc5OTU1MTY.*_ga_26G4XFTR63*MTcxNzk5NTUxNi4xLjEuMTcxNzk5OTgwNC4wLjAuMA..
856			_3Reviews _uhttps://www.goodreads.com/book/show/16700838-foundations-of-analysis?from_search=true&from_srp=true&qid=ueQKWDjgCy&rank=1#CommunityReviews
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