Metric Spaces Iteration and Application

ISBN-10: 0521318971
ISBN-13: 9780521318976
Edition: 1985
Authors: Victor W. Bryant
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Description: 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  More...

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Book details

List price: $39.99
Copyright year: 1985
Publisher: Cambridge University Press
Publication date: 5/2/1985
Binding: Paperback
Pages: 112
Size: 5.50" wide x 8.50" long x 0.25" tall
Weight: 2.002
Language: English

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.

Preface
Sequences by iteration
Where are we heading?
Sequences of numbers by iteration
Iterations in a different world
Metric spaces
Distance
Examples of metric spaces
Sequences
The three Cs
Iteration revisited
Closed sets
An internal test for convergence
Complete sets
Compact sets
The contraction mapping principle
Real fixed points
Contractions
Real contractions revisited
Some extensions
Differential equations
The implicit function theorem
Conclusion
What makes analysis work?
Continuity
Attained bounds
Uniform continuity
Inverse functions
Intermediate values
Some final remarks
Index

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