Mathematical Analysis and Proof - 2nd Edition - ISBN: 9781904275404, 9780857099341

Mathematical Analysis and Proof

2nd Edition

Authors: David S G Stirling
Paperback ISBN: 9781904275404
eBook ISBN: 9780857099341
Imprint: Woodhead Publishing
Published Date: 30th April 2009
Page Count: 262
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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.

Key Features

  • 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

Readership

University students

Table of Contents

  • Author’s Preface
  • 1: Setting the Scene
    • 1.1 Introduction
    • 1.2 The Common Number Systems
  • 2: Logic and Deduction
    • 2.1 Introduction
    • 2.2 Implication
    • 2.3 Is This All Necessary – or Worthwhile?
    • 2.4 Using the Right Words
  • 3: Mathematical Induction
    • 3.1 Introduction
    • 3.2 Arithmetic Progressions
    • 3.3 The Principle of Mathematical Induction
    • 3.4 Why All the Fuss About Induction?
    • 3.5 Examples of Induction
    • 3.6 The Binomial Theorem
  • 4: Sets and Numbers
    • 4.1 Sets
    • 4.2 Standard Sets
    • 4.3 Proof by Contradiction
    • 4.4 Sets Again
    • 4.5 Where We Have Got To – and The Way Ahead
    • 4.6 A Digression
  • 5: Order and Inequalities
    • 5.1 Basic Properties
    • 5.2 Consequences of the Basic Properties
    • 5.3 Bernoulli’s Inequality
    • 5.4 The Modulus (or Absolute Value)
  • 6: Decimals
    • 6.1 Decimal Notation
    • 6.2 Decimals of Real Numbers
    • 5.3 Some Interesting Consequences
  • 7: Limits
    • 7.1 The Idea of a Limit
    • 7.2 Manipulating Limits
    • 7.3 Developments
  • 8: Infinite Series
    • 8.1 Introduction
    • 8.2 Convergence Tests
    • 8.3 Power Series
    • 8.4 Decimals again
    • Problems
  • 9: The Structure of the Real Number System
    • Problems
  • 10: Continuity
    • 10.1 Introduction
    • 10.2 The Limit of a Function of a Real Variable
    • 10.3 Continuity
    • 10.4 Inverse Functions
    • 10.5 Some Discontinuous Functions
  • 11: Differentiation
    • 11.1 Basic Results
    • 11.2 The Mean Value Theorem and its Friends
    • 11.3 Approximating the Value of a Limit
  • 12: Functions Defined by Power Series
    • 12.1 Introduction
    • 12.2 Functions Defined by Power Series
    • 12.3 Some Standard Functions of Mathematics
    • 12.4 Further Examples
    • Problems
  • 13: Integration
    • 13.1 The Integral
    • 13.2 Approximating the Value of an Integral
    • 13.3 Improper Integrals
    • Problems
  • 14: Functions of Several Variables
    • 14.1 Continuity
    • 14.2 Differentiation
    • 14.3 Results Involving Interchange of Limits
    • 14.4 Solving Differential Equations
  • Appendix
    • The Expression of an Integer as a Decimal
  • Hints and Solutions to Selected Problems
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Chapter 6
    • Chapter 7
    • Chapter 8
    • Chapter 9
    • Chapter 10
    • Chapter 11
    • Chapter 12
    • Chapter 13
    • Chapter 14
  • Notation Index
  • Subject Index

Details

No. of pages:
262
Language:
English
Copyright:
© Woodhead Publishing 2009
Published:
Imprint:
Woodhead Publishing
eBook ISBN:
9780857099341
Paperback ISBN:
9781904275404

About the Author

David S G Stirling

Reviews

Carefully treads the fine line between accuracy and exactitude. A comprehensive introduction, very much in the classical mould, chatty and written with common student misunderstandings in mind. Should be in your undergraduate reference library., The Mathematical Gazette
Self-contained and one of the better books. I will definitely and without hesitation recommend and encourage other lecturers to give it serious consideration as a teaching aid., Mathematics Today