Real analysis : a constructive approach / Mark Bridger.

Format:

Book

Author/Creator:

Bridger, Mark, 1942-

Series:

Pure and applied mathematics (John Wiley & Sons : Unnumbered)

Pure and applied mathematics

Language:

English

Subjects (All):

Mathematical analysis.

Continuity.

Differentiable functions.

Physical Description:

xvi, 302 pages : illustrations ; 25 cm.

Place of Publication:

Hoboken, N.J. : Wiley-Interscience, [2012]

Summary:

"This innovative text sets forth a thoroughly rigorous modern account of the theoretical underpinnings of calculus: continuity, differentiability, and convergence. Using a constructive approach, every proof of every result is direct and ultimately computationally verifiable. In particular, existence is never established by showing that the assumption of non-existence leads to a contradiction. The ultimate consequence of this method is that it makes sense - not just to math majors but also to students from all branches of the sciences"--P. [4] of cover.

Contents:

Preliminaries

The natural numbers

The rationals

The real numbers and completeness

Introduction

Interval arithmetic

Families of intersecting intervals

Fine families

Definition of the reals

Real number arithmetic

Rational approximations

Real intervals and completeness

Limits and limiting families

Appendix: The Goldbach number and trichotomy

An inverse function theorem and its application

Functions and inverses

An inverse function theorem

The exponential function

Natural logs and the Euler number e

Limits, sequences and series

Sequences and convergence

Limits of functions

Series of numbers

Appendix I: Some properties of exp and log

Appendix II: Rearrangements of series

Uniform continuity

Definitions and elementary properties

Limits and extensions

Appendix I: Are there non-continuous functions?

Appendix II: Continuity of double-sided inverses

Appendix III: The Goldbach function

The Riemann integral

Definition and existence

elementary properties

Extensions and improper integrals

Differentiation

Definitions and basic properties

The arithmetic of differentiability

Two important theorems

Derivative tools

Integral tools

Sequences and series of functions

Sequences of functions

Integrals and derivatives of sequences

Power series

Taylor series

The periodic functions

Appendix: Binomial issues

The complex numbers and fourier series

The complex numbers C

Complex functions and vectors

Fourier series theory.

Notes:

Orignally published: 2007.

Includes bibliographical references (page 295) and index.

ISBN:

1118357064

9781118357064

OCLC:

784139765