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100 $a20121227d1997 u| 0
101 0 $aeng
135 $aurnn|008mamaa
181 $ctxt
182 $cc
183 $acr
200 10$aLimits$b[electronic resource] $eA New Approach to Real Analysis /$fby Alan F. Beardon
205 $a1st ed. 1997.
210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1997.
215 $a1 online resource (IX, 190 p.)
225 1 $aUndergraduate Texts in Mathematics,$x0172-6056
300 $aBibliographic Level Mode of Issuance: Monograph
311 $a0-387-98274-4
311 $a1-4612-6872-9
320 $aIncludes bibliographical references and index.
327 $aI 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.
330 $aBroadly speaking, analysis is the study of limiting processes such as sum ming infinite series and differentiating and integrating functions, and in any of these processes there are two issues to consider; first, there is the question of whether or not the limit exists, and second, assuming that it does, there is the problem of finding its numerical value. By convention, analysis is the study oflimiting processes in which the issue of existence is raised and tackled in a forthright manner. In fact, the problem of exis tence overshadows that of finding the value; for example, while it might be important to know that every polynomial of odd degree has a zero (this is a statement of existence), it is not always necessary to know what this zero is (indeed, if it is irrational, we may never know what its true value is). Despite the fact that this book has much in common with other texts on analysis, its approach to the subject differs widely from any other text known to the author. In other texts, each limiting process is discussed, in detail and at length before the next process. There are several disadvan tages in this approach. First, there is the need for a different definition for each concept, even though the student will ultimately realise that these different definitions have much in common.
410 0$aUndergraduate Texts in Mathematics,$x0172-6056
606 $aFunctions of real variables
606 $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171
615 0$aFunctions of real variables.
615 14$aReal Functions.
676 $a515.8
700 $aBeardon$b Alan F$4aut$4http://id.loc.gov/vocabulary/relators/aut$048923
906 $aBOOK
912 $a9910789345603321
996 $aLimits$983064
997 $aUNINA