








1. 
Record Nr. 
UNINA9910789345603321 


Autore 
Beardon Alan F 


Titolo 
Limits [[electronic resource] ] : A New Approach to Real Analysis / / by Alan F. Beardon 







Pubbl/distr/stampa 


New York, NY : , : Springer New York : , : Imprint : Springer, , 1997 







ISBN 






Edizione 
[1st ed. 1997.] 





Descrizione fisica 

1 online resource (IX, 190 p.) 






Collana 

Undergraduate Texts in Mathematics, , 01726056 






Disciplina 






Soggetti 

Functions of real variables 
Real Functions 








Lingua di pubblicazione 






Formato 
Materiale a stampa 





Livello bibliografico 
Monografia 





Note generali 

Bibliographic Level Mode of Issuance: Monograph 






Nota di bibliografia 

Includes bibliographical references and index. 






Nota di contenuto 

I 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. 








Sommario/riassunto 

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. 





 