
eBook - ePub
Real Analysis - An Introduction
Mathematical Arguments and Elementary Proof Techniques
- English
- ePUB (mobile friendly)
- Available on iOS & Android
eBook - ePub
Real Analysis - An Introduction
Mathematical Arguments and Elementary Proof Techniques
About this book
Designed for a broad spectrum of mathematics majors, not only those pursuing graduate school, this book also provides a thorough explanation of undergraduate Real Analysis. Through a developmentally appropriate narrative that integrates informal discussion, motivation, and basic proof writing approaches with mathematical rigor and clarity, the aim is to assist all students in learning more about the real number system and calculus theory.
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Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access Real Analysis - An Introduction by Michael Cullinane in PDF and/or ePUB format. We have over one million books available in our catalogue for you to explore.
Information
Table of contents
- Title Page
- Copyright
- Contents
- Frontmatter
- Contents
- 1âAlgebraic and order properties of the real numbers
- 2âAbsolute value and distance
- 3âThe natural numbers, the integers, and the rational numbers
- 4âThe completeness of the real numbers
- 5âFinite sets and infinite sets
- 6âThe nested intervals property
- 7âLimit points, closed sets, and open sets
- 8âConnected sets and compact sets
- 9âAn introduction to sequences and sequential convergence
- 10âMore about sequences and convergence
- 11âSubsequences
- 12âLimits of functions
- 13âAn introduction to continuous functions
- 14âMore about continuity
- 15âThe derivative
- 16âThe mean value theorem
- 17âTaylor polynomials
- 18âThe Riemann integral
- 19âCriteria for integrability
- 20âThe fundamental theorem of calculus
- 21âApproximating the value of an integral
- 22âInfinite series
- 23âAbsolute convergence and conditional convergence
- 24âRegroupings and rearrangements of series
- 25âSequences and series of functions
- 26âUniform convergence
- 27âMore about power series and Taylor series
- 28âThe trigonometric functions
- 29âTwo remarkable results of Weierstrass
- Index
- Subject Index