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...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Oxford :
OUP Oxford,
2012.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (217 pages) |
| ISBN: | 9780191627866 0191627860 1280595191 9781280595196 |
Internformat
MARC
| LEADER | 00000cam a2200000 a 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn784886666 | ||
| 003 | OCoLC | ||
| 005 | 20241004212047.0 | ||
| 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 |d OCLCL |d OCLCQ |d OCLCL | ||
| 019 | |a 817083215 | ||
| 020 | |a 9780191627866 |q (electronic bk.) | ||
| 020 | |a 0191627860 |q (electronic bk.) | ||
| 020 | |a 1280595191 | ||
| 020 | |a 9781280595196 | ||
| 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 | 7 | |a 515 |2 22 | |
| 049 | |a MAIN | ||
| 100 | 1 | |a Applebaum, David, |d 1956- |1 https://id.oclc.org/worldcat/entity/E39PBJy8y3QGCbgDCrfbc6hmBP |0 http://id.loc.gov/authorities/names/n95108612 | |
| 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. | |
| 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 | |
| 758 | |i has work: |a Limits, Limits Everywhere (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFCPyyFwgmq9dtMRhgg3gq |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 856 | 4 | 0 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=442898 |3 Volltext |
| 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 GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
| 049 | |a DE-863 | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn784886666 |
|---|---|
| _version_ | 1816881791034720256 |
| adam_text | |
| any_adam_object | |
| author | Applebaum, David, 1956- |
| author_GND | http://id.loc.gov/authorities/names/n95108612 |
| author_facet | Applebaum, David, 1956- |
| author_role | |
| author_sort | Applebaum, David, 1956- |
| author_variant | d a da |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA300 |
| callnumber-raw | QA300 .A67 2012eb |
| callnumber-search | QA300 .A67 2012eb |
| callnumber-sort | QA 3300 A67 42012EB |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | 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. 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. 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. 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. |
| ctrlnum | (OCoLC)784886666 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>05054cam a2200565 a 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn784886666</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20241004212047.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr cnu---unuuu</controlfield><controlfield tag="008">120409s2012 enk o 000 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">EBLCP</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">EBLCP</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">N$T</subfield><subfield code="d">YDXCP</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">IDEBK</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">DEBSZ</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCF</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">IGB</subfield><subfield code="d">AGLDB</subfield><subfield code="d">U3W</subfield><subfield code="d">D6H</subfield><subfield code="d">CN8ML</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">VTS</subfield><subfield code="d">S9I</subfield><subfield code="d">TKN</subfield><subfield code="d">STF</subfield><subfield code="d">DKC</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">M8D</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">AJS</subfield><subfield code="d">OCLCO</subfield><subfield code="d">UKAHL</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCL</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCL</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">817083215</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780191627866</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0191627860</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1280595191</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781280595196</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)784886666</subfield><subfield code="z">(OCoLC)817083215</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA300</subfield><subfield code="b">.A67 2012eb</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">005000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">034000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">515</subfield><subfield code="2">22</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Applebaum, David,</subfield><subfield code="d">1956-</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PBJy8y3QGCbgDCrfbc6hmBP</subfield><subfield code="0">http://id.loc.gov/authorities/names/n95108612</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Limits, Limits Everywhere :</subfield><subfield code="b">the Tools of Mathematical Analysis /</subfield><subfield code="c">David Applebaum.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Oxford :</subfield><subfield code="b">OUP Oxford,</subfield><subfield code="c">2012.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (217 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="347" ind1=" " ind2=" "><subfield code="a">data file</subfield><subfield code="2">rda</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="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.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="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.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="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.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="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.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="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.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Mathematical analysis</subfield><subfield code="v">Textbooks.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Calculus.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Mathematical Analysis.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Mathematical analysis</subfield><subfield code="2">fast</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="a">Textbooks</subfield><subfield code="2">fast</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">Limits, Limits Everywhere (Text)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCFCPyyFwgmq9dtMRhgg3gq</subfield><subfield code="4">https://id.oclc.org/worldcat/ontology/hasWork</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=442898</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH24244218</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest Ebook Central</subfield><subfield code="b">EBLB</subfield><subfield code="n">EBL886505</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">442898</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest MyiLibrary Digital eBook Collection</subfield><subfield code="b">IDEB</subfield><subfield code="n">362502</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">7584632</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| genre | Textbooks fast |
| genre_facet | Textbooks |
| id | ZDB-4-EBA-ocn784886666 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:18:19Z |
| institution | BVB |
| isbn | 9780191627866 0191627860 1280595191 9781280595196 |
| language | English |
| oclc_num | 784886666 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (217 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | OUP Oxford, |
| record_format | marc |
| spelling | Applebaum, David, 1956- https://id.oclc.org/worldcat/entity/E39PBJy8y3QGCbgDCrfbc6hmBP http://id.loc.gov/authorities/names/n95108612 Limits, Limits Everywhere : the Tools of Mathematical Analysis / David Applebaum. Oxford : OUP Oxford, 2012. 1 online resource (217 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier data file rda 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. 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. 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. 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. 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. Print version record. Mathematical analysis Textbooks. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Mathematical analysis fast Textbooks fast has work: Limits, Limits Everywhere (Text) https://id.oclc.org/worldcat/entity/E39PCFCPyyFwgmq9dtMRhgg3gq https://id.oclc.org/worldcat/ontology/hasWork FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=442898 Volltext |
| spellingShingle | Applebaum, David, 1956- Limits, Limits Everywhere : the Tools of Mathematical Analysis / 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. 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. 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. 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. Mathematical analysis Textbooks. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Mathematical analysis fast |
| title | Limits, Limits Everywhere : the Tools of Mathematical Analysis / |
| title_auth | Limits, Limits Everywhere : the Tools of Mathematical Analysis / |
| title_exact_search | Limits, Limits Everywhere : the Tools of Mathematical Analysis / |
| title_full | Limits, Limits Everywhere : the Tools of Mathematical Analysis / David Applebaum. |
| title_fullStr | Limits, Limits Everywhere : the Tools of Mathematical Analysis / David Applebaum. |
| title_full_unstemmed | Limits, Limits Everywhere : the Tools of Mathematical Analysis / David Applebaum. |
| title_short | Limits, Limits Everywhere : |
| title_sort | limits limits everywhere the tools of mathematical analysis |
| title_sub | the Tools of Mathematical Analysis / |
| topic | Mathematical analysis Textbooks. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Mathematical analysis fast |
| topic_facet | Mathematical analysis Textbooks. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Mathematical analysis Textbooks |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=442898 |
| work_keys_str_mv | AT applebaumdavid limitslimitseverywherethetoolsofmathematicalanalysis |