Mathematical Analysis and Proof ( 2 )

Publication series :2

Author: Stirling   David S G  

Publisher: Elsevier Science‎

Publication year: 2009

E-ISBN: 9780857099341

P-ISBN(Paperback): 9781904275404

P-ISBN(Hardback):  9781904275404

Subject: O17 Mathematical Analysis

Language: ENG

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Description

This fundamental and straightforward text addresses a weakness observed among present-day students, namely a lack of familiarity with formal proof. Beginning with the idea of mathematical proof and the need for it, associated technical and logical skills are developed with care and then brought to bear on the core material of analysis in such a lucid presentation that the development reads naturally and in a straightforward progression. Retaining the core text, the second edition has additional worked examples which users have indicated a need for, in addition to more emphasis on how analysis can be used to tell the accuracy of the approximations to the quantities of interest which arise in analytical limits.

  • Addresses a lack of familiarity with formal proof, a weakness observed among present-day mathematics students
  • Examines the idea of mathematical proof, the need for it and the technical and logical skills required

Chapter

Cover

pp.:  1 – 3

ABOUT THE AUTHOR

pp.:  3 – 4

Copyright

pp.:  5 – 6

Table of Contents

pp.:  6 – 8

Author's Preface

pp.:  8 – 10

1 Setting the Scene

pp.:  10 – 16

2 Logic and Deduction

pp.:  16 – 25

3 Mathematical Induction

pp.:  25 – 43

4 Sets and Numbers

pp.:  43 – 56

5 Order and Inequalities

pp.:  56 – 77

6 Decimals

pp.:  77 – 89

7 Limits

pp.:  89 – 106

8 Infinite Series

pp.:  106 – 120

9 The Structure of the Real Number System

pp.:  120 – 130

10 Continuity

pp.:  130 – 148

11 Differentiation

pp.:  148 – 168

12 Functions Defined by Power Series

pp.:  168 – 185

13 Integration

pp.:  185 – 211

14 Functions of Several Variables

pp.:  211 – 235

Appendix: The Expression of an Integer as a Decimal

pp.:  235 – 238

Hints and Solutions to Selected Problems

pp.:  238 – 256

Notation Index

pp.:  256 – 258

Subject Index

pp.:  258 – 263

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