Description

Book Synopsis
Real analysis provides the fundamental underpinnings for calculus, arguably the most useful and influential mathematical idea ever invented. It is a core subject in any mathematics degree, and also one which many students find challenging. A Sequential Introduction to Real Analysis gives a fresh take on real analysis by formulating all the underlying concepts in terms of convergence of sequences. The result is a coherent, mathematically rigorous, but conceptually simple development of the standard theory of differential and integral calculus ideally suited to undergraduate students learning real analysis for the first time.This book can be used as the basis of an undergraduate real analysis course, or used as further reading material to give an alternative perspective within a conventional real analysis course.

Table of Contents
Basic Properties of the Set or Real Numbers; Real Sequences; Limit Theorems; Subsequences; Series; Continuous Functions; Some Symbolic Logic; Limits of Functions; Differentiable Functions; Power Series; Integration; Logarithms and Irrational Powers; What are the Reals?;

Sequential Introduction To Real Analysis, A

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    A Paperback / softback by J Martin Speight

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      Book details

      Publisher Imperial College Press
      Published 31 December 2015
      ISBN-13 9781783267835
      978-1783267835
      ISBN-10 1783267836
      Also in:
      Real analysis, real variables

      Description

      Book Synopsis
      Real analysis provides the fundamental underpinnings for calculus, arguably the most useful and influential mathematical idea ever invented. It is a core subject in any mathematics degree, and also one which many students find challenging. A Sequential Introduction to Real Analysis gives a fresh take on real analysis by formulating all the underlying concepts in terms of convergence of sequences. The result is a coherent, mathematically rigorous, but conceptually simple development of the standard theory of differential and integral calculus ideally suited to undergraduate students learning real analysis for the first time.This book can be used as the basis of an undergraduate real analysis course, or used as further reading material to give an alternative perspective within a conventional real analysis course.

      Table of Contents
      Basic Properties of the Set or Real Numbers; Real Sequences; Limit Theorems; Subsequences; Series; Continuous Functions; Some Symbolic Logic; Limits of Functions; Differentiable Functions; Power Series; Integration; Logarithms and Irrational Powers; What are the Reals?;

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