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Metric Spaces

Iteration and Application

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Paperback | 1 July 1985

At a Glance

Paperback
112 Pages

Dimensions(cm)
21.6 x 14.2 x 0.7

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Here is an introductory text on metric spaces that is the first to be written for students who are as interested in the applications as in the theory. Knowledge of metric spaces is fundamental to understanding numerical methods (for example for solving differential equations) as well as analysis, yet most books at this level emphasise just the abstraction and theory. Dr Bryant uses applications to provide motivation and to sustain the development and discusses numerical procedures where appropriate. The reader is expected to have had some exposure to elementary analysis, but the author provides examples throughout to refresh the student's memory and to test and extend understanding. In short, this is an introductory textbook that will appeal to students of mathematics and engineering and will give them the required background for more advanced courses in both analysis and numerical analysis.

Industry Reviews

"...a fresh approach to a standard subject in topology and analysis...A healthy, vigorous introduction to analysis." American Scientist

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You Can Find This Book In

Non-Fiction Mathematics Topology Calculus & Mathematical Analysis Probability & Statistics

Preface	p. v
Sequences by iteration	p. 1
Where are we heading?	p. 1
Sequences of numbers by iteration	p. 1
Iterations in a different world	p. 7
Metric spaces	p. 12
Distance	p. 12
Examples of metric spaces	p. 14
Sequences	p. 22
The three Cs	p. 29
Iteration revisited	p. 29
Closed sets	p. 30
An internal test for convergence	p. 36
Complete sets	p. 38
Compact sets	p. 45
The contraction mapping principle	p. 52
Real fixed points	p. 52
Contractions	p. 57
Real contractions revisited	p. 62
Some extensions	p. 64
Differential equations	p. 71
The implicit function theorem	p. 83
Conclusion	p. 86
What makes analysis work?	p. 87
Continuity	p. 87
Attained bounds	p. 92
Uniform continuity	p. 94
Inverse functions	p. 96
Intermediate values	p. 98
Some final remarks	p. 103
Index	p. 105
Table of Contents provided by Syndetics. All Rights Reserved.

Metric Spaces

Iteration and Application

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

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