03399nam 22005295 450 001001700000005001700017010001800034024003000052035002600082035002400108035003400132035003200166035002500198035001900223035003200242035002300274035001900297035003000316100004000346101000800386135001800394181000800412182000600420183000700426200009000433205001800523210006700541215003600608225005100644300005200695311001900747311001900766320005100785327033200836330132601168410005102494606003202545606009502577615003302672615002002705676001002725700007602735906000902811912002102820996001802841997001002859991078934560332120200706012947.0 a1-4612-0697-97 a10.1007/978-1-4612-0697-2 a(CKB)3400000000089232 a(SSID)ssj0001297405 a(PQKBManifestationID)11756075 a(PQKBTitleCode)TC0001297405 a(PQKBWorkID)11374810 a(PQKB)11367085 a(DE-He213)978-1-4612-0697-2 a(MiAaPQ)EBC3074048 a(PPN)238005933 a(EXLCZ)993400000000089232 a20121227d1997 u| 00 aeng aurnn|008mamaa ctxt cc acr10aLimitsb[electronic resource] eA New Approach to Real Analysis /fby Alan F. Beardon a1st ed. 1997. 1aNew York, NY :cSpringer New York :cImprint: Springer,d1997. a1 online resource (IX, 190 p.) 1 aUndergraduate Texts in Mathematics,x0172-6056 aBibliographic Level Mode of Issuance: Monograph a0-387-98274-4 a1-4612-6872-9 aIncludes bibliographical references and index. 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. 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. 0aUndergraduate Texts in Mathematics,x0172-6056 aFunctions of real variables aReal Functions3https://scigraph.springernature.com/ontologies/product-market-codes/M12171 0aFunctions of real variables.14aReal Functions. a515.8 aBeardonb Alan F4aut4http://id.loc.gov/vocabulary/relators/aut048923 aBOOK a9910789345603321 aLimits983064 aUNINA