Course in Mathematical Analysis: Foundations and Elementary Real Analysis by D.J

Description: Course in Mathematical Analysis by D.J.H. Garling This is the first of three volumes that provide a full and detailed account of all those elements of real and complex analysis the undergraduate mathematics student can expect to encounter in their first two or three years of study. Numerous exercises, examples and applications are included. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and instructors. This first volume focuses on the analysis of real-valued functions of a real variable. Besides developing the basic theory it describes many applications, including a chapter on Fourier series. It also includes a Prologue in which the author introduces the axioms of set theory and uses them to construct the real number system. Volume 2 goes on to consider metric and topological spaces and functions of several variables. Volume 3 covers complex analysis and the theory of measure and integration. Author Biography D. J. H. Garling is an Emeritus Reader in Mathematical Analysis at the University of Cambridge and a Fellow of St Johns College, Cambridge. Table of Contents Introduction; Part I. Prologue: The Foundations of Analysis: 1. The axioms of set theory; 2. Number systems; Part II. Functions of a Real Variable: 3. Convergent sequences; 4. Infinite series; 5. The topology of R; 6. Continuity; 7. Differentiation; 8. Integration; 9. Introduction to Fourier series; 10. Some applications; Appendix: Zorns lemma and the well-ordering principle; Index. Review Garling is a gifted expositor and the book under review really conveys the beauty of the subject, not an easy task. [It] comes with appropriate examples when needed and has plenty of well-chosen exercises as may be expected from a textbook. As the author points out in the introduction, a newcomer may be advised, on a first reading, to skip part one and take the required properties of the ordered real field as axioms; later on, as the student matures, he/she may go back to a detailed reading of the skipped part. This is good advice. Felipe Zaldivar, MAA Reviews This work is the first in a three-volume set dedicated to real and complex analysis that mathematical undergraduates may expect to meet in the first two years or so ... of analysis ... The exposition is superb: open and nontelegraphic. Highly recommended. Upper-division undergraduates and graduate students. D. Robbins, Choice These three volumes cover very thoroughly the whole of undergraduate analysis and much more besides. John Baylis, The Mathematical Gazette "Garling is a gifted expositor and the book under review really conveys the beauty of the subject, not an easy task. [It] comes with appropriate examples when needed and has plenty of well-chosen exercises as may be expected from a textbook. As the author points out in the introduction, a newcomer may be advised, on a first reading, to skip part one and take the required properties of the ordered real field as axioms; later on, as the student matures, he/she may go back to a detailed reading of the skipped part. This is good advice." Felipe Zaldivar, MAA Reviews "This work is the first in a three-volume set dedicated to real and complex analysis that "mathematical undergraduates may expect to meet in the first two years or so ... of analysis" ... The exposition is superb: open and nontelegraphic. Highly recommended. Upper-division undergraduates and graduate students." D. Robbins, Choice "These three volumes cover very thoroughly the whole of undergraduate analysis and much more besides." John Baylis, The Mathematical Gazette Review Quote "Garling is a gifted expositor and the book under review really conveys the beauty of the subject, not an easy task. [It] comes with appropriate examples when needed and has plenty of well-chosen exercises as may be expected from a textbook. As the author points out in the introduction, a newcomer may be advised, on a first reading, to skip part one and take the required properties of the ordered real field as axioms; later on, as the student matures, he/she may go back to a detailed reading of the skipped part. This is good advice." Felipe Zaldivar, MAA Reviews Promotional "Headline" The first volume of three providing a full and detailed account of undergraduate mathematical analysis. Description for Bookstore This is the first of three volumes that provide a full and detailed account of all those elements of real and complex analysis the undergraduate mathematics student can expect to encounter in their first two or three years of study. Numerous exercises, examples and applications are included. Description for Library This is the first of three volumes that provide a full and detailed account of all those elements of real and complex analysis the undergraduate mathematics student can expect to encounter in their first two or three years of study. Numerous exercises, examples and applications are included. Details ISBN1107032024 Year 2013 ISBN-10 1107032024 ISBN-13 9781107032026 Media Book Publisher CAMBRIDGE UNIVERSITY PRESS Language English DEWEY 515 Short Title COURSE IN MATHEMATICAL ANALYSI Publication Date 2013-04-25 Imprint Cambridge University Press Place of Publication Cambridge Country of Publication United Kingdom Pages 318 Series A Course in Mathematical Analysis 3 Volume Set Illustrations Worked examples or Exercises; 21 Line drawings, unspecified Subtitle Foundations and Elementary Real Analysis Audience College/Higher Education UK Release Date 2013-04-25 AU Release Date 2013-04-25 NZ Release Date 2013-04-25 Author D.J.H. Garling Format Hardcover We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:91396240;

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