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Undergraduate analysis : a working textbook /
An innovative self-contained Analysis textbook for undergraduates, that takes advantage of proven successful educational techniques.
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford, United Kingdom :
Oxford University Press,
2018.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000 i 4500 | ||
|---|---|---|---|
| 001 | EBSCO_on1034724536 | ||
| 003 | OCoLC | ||
| 005 | 20231017213018.0 | ||
| 006 | m o d | ||
| 007 | cr cnu|||unuuu | ||
| 008 | 180507s2018 enk ob 001 0 eng d | ||
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| 066 | |c (S | ||
| 019 | |a 1035364272 | ||
| 020 | |a 9780192549839 |q (electronic bk.) | ||
| 020 | |a 0192549839 |q (electronic bk.) | ||
| 020 | |z 9780198817574 |q (print) | ||
| 020 | |z 0198817568 | ||
| 020 | |z 9780198817567 | ||
| 020 | |z 0198817576 | ||
| 035 | |a (OCoLC)1034724536 |z (OCoLC)1035364272 | ||
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| 049 | |a UAMI | ||
| 100 | 1 | |a McCluskey, Aisling, |e author. | |
| 245 | 1 | 0 | |a Undergraduate analysis : |b a working textbook / |c Aisling McCluskey, Brian McMaster. |
| 264 | 1 | |a Oxford, United Kingdom : |b Oxford University Press, |c 2018. | |
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Online resource; title from PDF title page (Ebsco, viewed May 10, 2018). | |
| 505 | 8 | |6 880-01 |a 2.9 POSTSCRIPT: to infinity2.10 Important note on 'elementary functions'; 3 Interlude: different kinds of numbers; 3.1 Sets; 3.2 Intervals, max and min, sup and inf; 3.3 Denseness; 4 Up and down -- increasing and decreasing sequences; 4.1 Monotonic bounded sequences must converge; 4.2 Induction: infinite returns for finite effort; 4.3 Recursively defined sequences; 4.4 POSTSCRIPT: The epsilontics game -- the 'fifth factor of difficulty'; 5 Sampling a sequence -- subsequences; 5.1 Introduction; 5.2 Subsequences; 5.3 Bolzano-Weierstrass: the overcrowded interval | |
| 505 | 8 | |a 6 Special (or specially awkward) examples6.1 Introduction; 6.2 Important examples of convergence; 7 Endless sums -- a first look at series; 7.1 Introduction; 7.2 Definition and easy results; 7.3 Big series, small series: comparison tests; 7.4 The root test and the ratio test; 8 Continuous functions -- the domain thinks that the graph is unbroken; 8.1 Introduction; 8.2 An informal view of continuity; 8.3 Continuity at a point; 8.4 Continuity on a set; 8.5 Key theorems on continuity; 8.6 Continuity of the inverse; 9 Limit of a function; 9.1 Introduction; 9.2 Limit of a function at a point | |
| 505 | 8 | |a 10 Epsilontics and functions10.1 The epsilontic view of function limits; 10.2 The epsilontic view of continuity; 10.3 One-sided limits; 11 Infinity and function limits; 11.1 Limit of a function as x tends to infinity or minus infinity; 11.2 Functions tending to infinity or minus infinity; 12 Differentiation -- the slope of the graph; 12.1 Introduction; 12.2 The derivative; 12.3 Up and down, maximum and minimum: for differentiable functions; 12.4 Higher derivatives; 12.5 Alternative proof of the chain rule; 13 The Cauchy condition -- sequences whose terms pack tightly together | |
| 505 | 8 | |a 13.1 Cauchy equals convergent14 More about series; 14.1 Absolute convergence; 14.2 The 'robustness' of absolutely convergent series; 14.3 Power series; 15 Uniform continuity -- continuity's global cousin; 15.1 Introduction; 15.2 Uniformly continuous functions; 15.3 The bounded derivative test; 16 Differentiation -- mean value theorems, power series; 16.1 Introduction; 16.2 Cauchy and l'Hôpital; 16.3 Taylor series; 16.4 Differentiating a power series; 17 Riemann integration -- area under a graph; 17.1 Introduction | |
| 505 | 8 | |a 17.2 Riemann integrability -- how closely can rectangles approximate areas under graphs? | |
| 520 | |a An innovative self-contained Analysis textbook for undergraduates, that takes advantage of proven successful educational techniques. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Mathematical analysis. | |
| 650 | 6 | |a Analyse mathématique. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Mathematical analysis |2 fast | |
| 700 | 1 | |a McMaster, Brian, |e author. | |
| 776 | 0 | 8 | |i Print version: |a McCluskey, Aisling. |t Undergraduate analysis. |d Oxford, United Kingdom : Oxford University Press, 2018 |z 0198817568 |z 9780198817567 |w (OCoLC)1013489598 |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1803902 |z Texto completo |
| 880 | 0 | |6 505-01/(S |a Cover; Undergraduate Analysis: A Working Textbook; Copyright; Dedication; Preface; Contents; A Note to the Instructor; A Note to the Student Reader; 1 Preliminaries; 1.1 Real numbers; 1.2 The basic rules of inequalities -- a checklist of things you probably know already; 1.3 Modulus; 1.4 Floor; 2 Limit of a sequence -- an idea, a definition, a tool; 2.1 Introduction; 2.2 Sequences, and how to write them; 2.3 Approximation; 2.4 Infinite decimals; 2.5 Approximating an area; 2.6 A small slice of π; 2.7 Testing limits by the definition; 2.8 Combining sequences; the algebra of limits | |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH37166846 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL5378475 | ||
| 938 | |a EBSCOhost |b EBSC |n 1803902 | ||
| 938 | |a YBP Library Services |b YANK |n 15343378 | ||
| 994 | |a 92 |b IZTAP | ||