Coverart for item
The Resource Limits, Limits Everywhere : the Tools of Mathematical Analysis, David Applebaum

Limits, Limits Everywhere : the Tools of Mathematical Analysis, David Applebaum

Label
Limits, Limits Everywhere : the Tools of Mathematical Analysis
Title
Limits, Limits Everywhere
Title remainder
the Tools of Mathematical Analysis
Statement of responsibility
David Applebaum
Creator
Subject
Genre
Language
eng
Summary
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
Cataloging source
EBLCP
http://library.link/vocab/creatorDate
1956-
http://library.link/vocab/creatorName
Applebaum, David
Dewey number
515
Index
no index present
LC call number
QA300
LC item number
.A67 2012eb
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/subjectName
  • Mathematical analysis
  • MATHEMATICS
  • MATHEMATICS
  • Mathematical analysis
Label
Limits, Limits Everywhere : the Tools of Mathematical Analysis, David Applebaum
Instantiates
Publication
Antecedent source
unknown
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Control code
784886666
Dimensions
unknown
Extent
1 online resource (217 pages)
File format
unknown
Form of item
online
Isbn
9780191627866
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)784886666
Label
Limits, Limits Everywhere : the Tools of Mathematical Analysis, David Applebaum
Publication
Antecedent source
unknown
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Control code
784886666
Dimensions
unknown
Extent
1 online resource (217 pages)
File format
unknown
Form of item
online
Isbn
9780191627866
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)784886666

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