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Undergraduate Texts in Mathematics Ser.: Limits : A New Approach to Real Analysis by Alan F. Beardon (1997, Hardcover)
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Limits : A New Approach to Real Analysis, Hardcover by Beardon, Alan F., ISBN 0387982744, ISBN-13 9780387982748, Brand New, Free shipping in the US This book is intended as an undergraduate text on real analysis and includes all the standard material such as sequences, infinite series, continuity, differentiation, and integration, together with worked examples and exercises. By unifying and simplifying all the various notions of limit, the author has successfully presented a unique and novel approach to the subject matter, which will lead to a better understanding on the part of students.
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About this product
Product Identifiers
PublisherSpringer New York
ISBN-100387982744
ISBN-139780387982748
eBay Product ID (ePID)738502
Product Key Features
Number of PagesIX, 190 Pages
LanguageEnglish
Publication NameLimits : a New Approach to Real Analysis
Publication Year1997
SubjectMathematical Analysis
TypeTextbook
Subject AreaMathematics
AuthorAlan F. Beardon
SeriesUndergraduate Texts in Mathematics Ser.
FormatHardcover
Dimensions
Item Height0.2 in
Item Weight36.3 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN97-020490
Dewey Edition21
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal515/.222
Table Of ContentI Foundations.- 1 Sets and Functions.- 2 Real and Complex Numbers.- II Limits.- 3 Limits.- 4 Bisection Arguments.- 5 Infinite Series.- 6 Periodic Functions.- III Analysis.- 7 Sequences.- 8 Continuous Functions.- 9 Derivatives.- 10 Integration.- 11 ?, ?, e, and n!.- Appendix: Mathematical Induction.- References.
SynopsisBroadly speaking, analysis is the study of limiting processes such as sum- ming infinite series and differentiating and integrating functions, and in any of these processes there are two issues to consider; first, there is the question of whether or not the limit exists, and second, assuming that it does, there is the problem of finding its numerical value. By convention, analysis is the study oflimiting processes in which the issue of existence is raised and tackled in a forthright manner. In fact, the problem of exis- tence overshadows that of finding the value; for example, while it might be important to know that every polynomial of odd degree has a zero (this is a statement of existence), it is not always necessary to know what this zero is (indeed, if it is irrational, we may never know what its true value is). Despite the fact that this book has much in common with other texts on analysis, its approach to the subject differs widely from any other text known to the author. In other texts, each limiting process is discussed, in detail and at length before the next process. There are several disadvan- tages in this approach. First, there is the need for a different definition for each concept, even though the student will ultimately realise that these different definitions have much in common., Broadly speaking, analysis is the study of limiting processes such as sum ming infinite series and differentiating and integrating functions, and in any of these processes there are two issues to consider; first, there is the question of whether or not the limit exists, and second, assuming that it does, there is the problem of finding its numerical value. By convention, analysis is the study oflimiting processes in which the issue of existence is raised and tackled in a forthright manner. In fact, the problem of exis tence overshadows that of finding the value; for example, while it might be important to know that every polynomial of odd degree has a zero (this is a statement of existence), it is not always necessary to know what this zero is (indeed, if it is irrational, we may never know what its true value is). Despite the fact that this book has much in common with other texts on analysis, its approach to the subject differs widely from any other text known to the author. In other texts, each limiting process is discussed, in detail and at length before the next process. There are several disadvan tages in this approach. First, there is the need for a different definition for each concept, even though the student will ultimately realise that these different definitions have much in common., This book is intended as an undergraduate text on real analysis and includes all the standard material such as sequences, infinite series, continuity, differentiation, and integration, together with worked examples and exercises. By unifying and simplifying all the various notions of limit, the author has successfully presented a unique and novel approach to the subject matter, which will lead to a better understanding on the part of students.
LC Classification NumberQA331.5
