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Metric Spaces : Iteration and Application - Victor Bryant

Metric Spaces

Iteration and Application

Paperback Published: 1st July 1985
ISBN: 9780521318976
Number Of Pages: 112

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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.

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

Prefacep. v
Sequences by iterationp. 1
Where are we heading?p. 1
Sequences of numbers by iterationp. 1
Iterations in a different worldp. 7
Metric spacesp. 12
Distancep. 12
Examples of metric spacesp. 14
Sequencesp. 22
The three Csp. 29
Iteration revisitedp. 29
Closed setsp. 30
An internal test for convergencep. 36
Complete setsp. 38
Compact setsp. 45
The contraction mapping principlep. 52
Real fixed pointsp. 52
Contractionsp. 57
Real contractions revisitedp. 62
Some extensionsp. 64
Differential equationsp. 71
The implicit function theoremp. 83
Conclusionp. 86
What makes analysis work?p. 87
Continuityp. 87
Attained boundsp. 92
Uniform continuityp. 94
Inverse functionsp. 96
Intermediate valuesp. 98
Some final remarksp. 103
Indexp. 105
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521318976
ISBN-10: 0521318971
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 112
Published: 1st July 1985
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 21.6 x 13.8  x 0.7
Weight (kg): 0.15