UID:
almahu_9948025571602882
Umfang:
1 online resource (262 p.)
Ausgabe:
2nd ed.
ISBN:
0-85709-934-5
Inhalt:
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
Anmerkung:
"First published by Horwood Publishing Limited, 1997"--T.p. verso.
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Includes indexes.
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Cover; ABOUT THE AUTHOR; MATHEMATICAL ANALYSIS AND PROOF; Copyright; 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; Problems; 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; Problems; 4 Sets and Numbers; 4.1 Sets; 4.2 Standard Sets
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4.3 Proof by Contradiction4.4 Sets Again; 4.5 Where We Have Got To - and The Way Ahead; 4.6 A Digression; Problems; 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); Problems; 6 Decimals; 6.1 Decimal Notation; 6.2 Decimals of Real Numbers; 6.3 Some Interesting Consequences; Problems; 7 Limits; 7.1 The Idea of a Limit; 7.2 Manipulating Limits; 7.3 Developments; Problems; 8 Infinite Series; 8.1 Introduction; 8.2 Convergence Tests; 8.3 Power Series; 8.4 Decimals again; Problems
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9 The Structure of the Real Number SystemProblems; 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; Problems; 11 Differentiation; 11.1 Basic Results; 11.2 The Mean Value Theorem and its Friends; 11.3 Approximating the Value of a Limit; Problems; 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
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13.2 Approximating the Value of an Integral13.3 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; Problems; Appendix: The Expression of an Integer as a Decimal; References; Further Reading; 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
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English
Weitere Ausg.:
ISBN 1-904275-40-0
Sprache:
Englisch
