Cargando…
Limits, Limits Everywhere : the Tools of Mathematical Analysis /
A quantity can be made smaller and smaller without it ever vanishing. This fact has profound consequences for science, technology, and even the way we think about numbers. In this book, we will explore this idea by moving at an easy pace through an account of elementary real analysis and, in particu...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford :
OUP Oxford,
2012.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000Ia 4500 | ||
|---|---|---|---|
| 001 | EBSCO_ocn784886666 | ||
| 003 | OCoLC | ||
| 005 | 20231017213018.0 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 120409s2012 enk o 000 0 eng d | ||
| 040 | |a EBLCP |b eng |e pn |c EBLCP |d OCLCQ |d N$T |d YDXCP |d OCLCQ |d IDEBK |d OCLCQ |d DEBSZ |d OCLCQ |d OCLCF |d OCLCQ |d IGB |d AGLDB |d U3W |d D6H |d CN8ML |d OCLCQ |d VTS |d S9I |d TKN |d STF |d DKC |d OCLCQ |d M8D |d OCLCQ |d AJS |d OCLCO |d UKAHL |d OCLCQ |d OCLCO | ||
| 019 | |a 817083215 | ||
| 020 | |a 9780191627866 |q (electronic bk.) | ||
| 020 | |a 0191627860 |q (electronic bk.) | ||
| 020 | |a 1280595191 | ||
| 020 | |a 9781280595196 | ||
| 029 | 1 | |a AU@ |b 000055806171 | |
| 029 | 1 | |a DEBSZ |b 37932704X | |
| 029 | 1 | |a DEBSZ |b 445111038 | |
| 029 | 1 | |a NZ1 |b 14534083 | |
| 035 | |a (OCoLC)784886666 |z (OCoLC)817083215 | ||
| 050 | 4 | |a QA300 |b .A67 2012eb | |
| 072 | 7 | |a MAT |x 005000 |2 bisacsh | |
| 072 | 7 | |a MAT |x 034000 |2 bisacsh | |
| 082 | 0 | 4 | |a 515 |2 22 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Applebaum, David, |d 1956- | |
| 245 | 1 | 0 | |a Limits, Limits Everywhere : |b the Tools of Mathematical Analysis / |c David Applebaum. |
| 260 | |a Oxford : |b OUP Oxford, |c 2012. | ||
| 300 | |a 1 online resource (217 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a data file |2 rda | ||
| 505 | 0 | |a Cover; Contents; PART I: APPROACHING LIMITS; 1. A Whole Lot of Numbers; 1.1 Natural Numbers; 1.2 Prime Numbers; 1.3 The Integers; 1.4 Exercises for Chapter 1; 2. Let's Get Real; 2.1 The Rational Numbers; 2.2 Irrational Numbers; 2.3 The Real Numbers; 2.4 A First Look at Infinity; 2.5 Exercises for Chapter 2; 3. The Joy of Inequality; 3.1 Greater or Less?; 3.2 Intervals; 3.3 The Modulus of a Number; 3.4 Maxima and Minima; 3.5 The Theorem of the Means; 3.6 Getting Closer; 3.7 Exercises for Chapter 3; 4. Where Do You Go To, My Lovely?; 4.1 Limits; 4.2 Bounded Sequences; 4.3 The Algebra of Limits. | |
| 505 | 8 | |a 4.4 Fibonacci Numbers and the Golden Section4.5 Exercises for Chapter 4; 5. Bounds for Glory; 5.1 Bounded Sequences Revisited; 5.2 Monotone Sequences; 5.3 An Old Friend Returns; 5.4 Finding Square Roots; 5.5 Exercises for Chapter 5; 6. You Cannot be Series; 6.1 What are Series?; 6.2 The Sigma Notation; 6.3 Convergence of Series; 6.4 Nonnegative Series; 6.5 The Comparison Test; 6.6 Geometric Series; 6.7 The Ratio Test; 6.8 General Infinite Series; 6.9 Conditional Convergence; 6.10 Regrouping and Rearrangements; 6.11 Real Numbers and Decimal Expansions; 6.12 Exercises for Chapter 6. | |
| 505 | 8 | |a PART II: EXPLORING LIMITS7. Wonderful Numbers -- e, p and?; 7.1 The Number e; 7.2 The Number p; 7.3 The Number?; 8. Infinite Products; 8.1 Convergence of Infinite Products; 8.2 Infinite Products and Prime Numbers; 8.3 Diversion -- Complex Numbers and the Riemann Hypothesis; 9. Continued Fractions; 9.1 Euclid's Algorithm; 9.2 Rational and Irrational Numbers as Continued Fractions; 10. How Infinite Can You Get?; 11. Constructing the Real Numbers; 11.1 Dedekind Cuts; 11.2 Cauchy Sequences; 11.3 Completeness; 12. Where to Next in Analysis? The Calculus; 12.1 Functions; 12.2 Limits and Continuity. | |
| 505 | 8 | |a 12.3 Differentiation12.4 Integration; 13. Some Brief Remarks About the History of Analysis; Further Reading; Appendices; Appendix 1: The Binomial Theorem; Appendix 2: The Language of Set Theory; Appendix 3: Proof by Mathematical Induction; Appendix 4: The Algebra of Numbers; Hints and Solutions to Selected Exercise; Index; A; B; C; D; E; F; G; H; I; J; K; L; M; N; O; P; Q; R; S; T; U; V; W; Z. | |
| 520 | |a A quantity can be made smaller and smaller without it ever vanishing. This fact has profound consequences for science, technology, and even the way we think about numbers. In this book, we will explore this idea by moving at an easy pace through an account of elementary real analysis and, in particular, will focus on numbers, sequences, and series. Almost all textbooks on introductory analysis assume some background in calculus. This book doesn't and, instead, the emphasis is on the application of analysis to number theory. The book is split into two parts. Part 1 follows a standard university. | ||
| 588 | 0 | |a Print version record. | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Mathematical analysis |v Textbooks. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Mathematical analysis |2 fast | |
| 655 | 7 | |a Textbooks |2 fast | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=442898 |z Texto completo |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH24244218 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL886505 | ||
| 938 | |a EBSCOhost |b EBSC |n 442898 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n 362502 | ||
| 938 | |a YBP Library Services |b YANK |n 7584632 | ||
| 994 | |a 92 |b IZTAP | ||