LEADER 03399nam 22005295 450 001 9910480083503321 005 20200706012947.0 010 $a1-4612-0697-9 024 7 $a10.1007/978-1-4612-0697-2 035 $a(CKB)3400000000089232 035 $a(SSID)ssj0001297405 035 $a(PQKBManifestationID)11756075 035 $a(PQKBTitleCode)TC0001297405 035 $a(PQKBWorkID)11374810 035 $a(PQKB)11367085 035 $a(DE-He213)978-1-4612-0697-2 035 $a(MiAaPQ)EBC3074048 035 $a(PPN)238005933 035 $a(EXLCZ)993400000000089232 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 $a9910480083503321 996 $aLimits$983064 997 $aUNINA