
Mathematical Analysis and Proof
Description
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
Table of Contents
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
Product details
- No. of pages: 262
- Language: English
- Copyright: © Woodhead Publishing 2009
- Published: April 30, 2009
- Imprint: Woodhead Publishing
- eBook ISBN: 9780857099341
About the Author
David S G Stirling
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